ବୋର୍ଡ ଅଫ୍ ସେକେଣ୍ଡାରୀ ଏଜୁକେସନ୍ (BSE Odisha) — ସମ୍ପୂର୍ଣ୍ଣ ଅଧ୍ୟାୟ ମାଷ୍ଟର ନୋଟ୍ସ
ଶ୍ରେଣୀ: Class 9 | ବିଷୟ: Physical Science
ଅଧ୍ୟାୟ: Class9 PhySci Ch08 Karjya O Sakti (କାର୍ଯ୍ୟ ଓ ଶକ୍ତି)
୧. ଅଧ୍ୟାୟର ସାରାଂଶ ଓ ମାଇଣ୍ଡ ମ୍ୟାପ୍ (Mind Map & Conceptual Architecture)
ଏହି ଅଧ୍ୟାୟଟି କାର୍ଯ୍ୟ (Work) ଓ ଶକ୍ତି (Energy) ର ମୌଳିକ ଧାରଣା ଉପରେ ଆଧାରିତ । ଦୈନନ୍ଦିନ ଜୀବନରେ ଆମେ କାର୍ଯ୍ୟ ଓ ଶକ୍ତିକୁ ଯେପରି ବୁଝୁ, ବିଜ୍ଞାନରେ ତାହାର ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ସଂଜ୍ଞା ଓ ଅର୍ଥ ରହିଛି । ଏହି ଅଧ୍ୟାୟରେ କାର୍ଯ୍ୟର ବୈଜ୍ଞାନିକ ସଂଜ୍ଞା, ଏହା ସମ୍ପାଦିତ ହେବା ପାଇଁ ଆବଶ୍ୟକ ସର୍ତ୍ତ, ଏହାର ପ୍ରକାରଭେଦ ଏବଂ ଏକକ ବିଷୟରେ ଆଲୋଚନା କରାଯାଇଛି । ଶକ୍ତିକୁ କାର୍ଯ୍ୟ କରିବାର ସାମର୍ଥ୍ୟ ଭାବରେ ବର୍ଣ୍ଣନା କରାଯାଇଛି ଏବଂ ଏହାର ବିଭିନ୍ନ ରୂପ ଯଥା ଗତିଜ ଶକ୍ତି (Kinetic Energy) ଓ ସ୍ଥିତିଜ ଶକ୍ତି (Potential Energy) ଉପରେ ବିସ୍ତୃତ ଭାବରେ ଆଲୋଚନା କରାଯାଇଛି । ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମ (Law of Conservation of Energy) ଏହି ଅଧ୍ୟାୟର ଏକ ଗୁରୁତ୍ୱପୂର୍ଣ୍ଣ ବିଷୟ । ଶେଷରେ, କାର୍ଯ୍ୟ କରିବାର ହାର ବା କ୍ଷମତା (Power) ଏବଂ ଶକ୍ତିର ବ୍ୟବସାୟିକ ଏକକ (Commercial Unit of Energy) ବିଷୟରେ ବର୍ଣ୍ଣନା କରାଯାଇଛି ।
ମୁଖ୍ୟ ଉଦ୍ଦେଶ୍ୟ:
ମାଇଣ୍ଡ ମ୍ୟାପ୍ (Conceptual Mind Map):
କାର୍ଯ୍ୟ ଓ ଶକ୍ତି
├── କାର୍ଯ୍ୟ (Work)
│ ├── ସଂଜ୍ଞା (ବଳ ଓ ବିସ୍ଥାପନ)
│ ├── ସର୍ତ୍ତ (ବଳ, ବିସ୍ଥାପନ)
│ ├── ପ୍ରକାରଭେଦ (ଯୁକ୍ତାତ୍ମକ, ବିଯୁକ୍ତାତ୍ମକ, ଶୂନ)
│ ├── ସୂତ୍ର (W = F × s)
│ └── ଏକକ (ଜୁଲ୍, ଅର୍ଗ; 1 J = 10⁷ Erg)
├── ଶକ୍ତି (Energy)
│ ├── ସଂଜ୍ଞା (କାର୍ଯ୍ୟ କରିବାର ସାମର୍ଥ୍ୟ)
│ ├── ଏକକ (ଜୁଲ୍)
│ ├── ଉତ୍ସ (ସୂର୍ଯ୍ୟ, ଅଣୁ, ପରମାଣୁ, ପବନ, ଜୁଆର ଇତ୍ୟାଦି)
│ ├── ପ୍ରକାରଭେଦ
│ │ ├── ଗତିଜ ଶକ୍ତି (Kinetic Energy)
│ │ │ ├── ସଂଜ୍ଞା (ଗତି ଯୋଗୁଁ ଶକ୍ତି)
│ │ │ ├── ସୂତ୍ର (E_k = (1/2)mv²)
│ │ │ └── ଉଦାହରଣ (ଚାଲୁଥିବା କାର୍, ଉଡ଼ାଜାହାଜ)
│ │ └── ସ୍ଥିତିଜ ଶକ୍ତି (Potential Energy)
│ │ ├── ସଂଜ୍ଞା (ଅବସ୍ଥାନ/ବିନ୍ୟାସ ଯୋଗୁଁ ଶକ୍ତି)
│ │ ├── ମାଧ୍ୟାକର୍ଷଣୀୟ ସ୍ଥିତିଜ ଶକ୍ତି (E_p = mgh)
│ │ └── ଉଦାହରଣ (ଉଚ୍ଚତାରେ ଥିବା ବସ୍ତୁ, ଟଣା ରବର)
│ └── ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମ (Law of Conservation of Energy)
│ ├── ସଂଜ୍ଞା (ସୃଷ୍ଟି/ବିନାଶ ନାହିଁ, ରୂପାନ୍ତରଣ)
│ ├── ଯାନ୍ତ୍ରିକ ଶକ୍ତି ସଂରକ୍ଷଣ (E_p + E_k = ସ୍ଥିର)
│ └── ଉଦାହରଣ (ମୁକ୍ତ ପତନ)
├── କ୍ଷମତା (Power)
│ ├── ସଂଜ୍ଞା (କାର୍ଯ୍ୟ କରିବାର ହାର)
│ ├── ସୂତ୍ର (P = W / t)
│ ├── ଏକକ (ୱାଟ୍, କିଲୋୱାଟ୍)
│ └── ହାରାହାରି କ୍ଷମତା
└── ଶକ୍ତିର ବ୍ୟବସାୟିକ ଏକକ (Commercial Unit of Energy)
├── କିଲୋୱାଟ ଘଣ୍ଟା (kWh)
└── ସମ୍ପର୍କ (1 kWh = 3.6 × 10⁶ J)
୨. ମୁଖ୍ୟ ବିଷୟବସ୍ତୁ, ସିଦ୍ଧାନ୍ତ ଓ ଗାଣିତିକ ସୂତ୍ରାବଳୀ (Comprehensive Theory & Formulas)
୨.୧ କାର୍ଯ୍ୟ (Work)
୨.୧.୧ କାର୍ଯ୍ୟର ବୈଜ୍ଞାନିକ ସଂଜ୍ଞା (Scientific Concept of Work):
ଦୈନନ୍ଦିନ ଜୀବନରେ ଆମେ କାର୍ଯ୍ୟ ଶବ୍ଦଟିକୁ ଯେପରି ବୁଝୁ, ବିଜ୍ଞାନରେ ତାହାର ଅର୍ଥ ଭିନ୍ନ । ବିଜ୍ଞାନ ଅନୁଯାୟୀ, କାର୍ଯ୍ୟ ସମ୍ପାଦନ ପାଇଁ ନିମ୍ନଲିଖିତ ଦୁଇଟି ସର୍ତ୍ତ ପୂରଣ ହେବା ଆବଶ୍ୟକ:
୧. ବସ୍ତୁ ଉପରେ ବଳ ପ୍ରୟୋଗ ହେବା ଆବଶ୍ୟକ ।
୨. ବଳ ପ୍ରୟୋଗ ହେବା ଦ୍ୱାରା ବସ୍ତୁର ବିସ୍ଥାପନ ଘଟିବା ଆବଶ୍ୟକ ।
ଯଦି ଏହି ଦୁଇଟି ସର୍ତ୍ତ ମଧ୍ୟରୁ କୌଣସି ଗୋଟିଏ ପୂରଣ ନହୁଏ, ତେବେ ବିଜ୍ଞାନ ଅନୁଯାୟୀ କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହୋଇନାହିଁ । ଉଦାହରଣ ସ୍ୱରୂପ, କାନ୍ଥକୁ ଠେଲିବା, ମୁଣ୍ଡରେ ବୋଝ ମୁଣ୍ଡେଇ ଠିଆ ହେବା ଇତ୍ୟାଦି କ୍ଷେତ୍ରରେ ବିସ୍ଥାପନ ନଥିବାରୁ କାର୍ଯ୍ୟ ହୁଏନାହିଁ ।
୨.୧.୨ ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ବଳ ଦ୍ୱାରା ସମ୍ପାଦିତ କାର୍ଯ୍ୟ (Work Done by a Constant Force):
ଯେତେବେଳେ ଏକ ବସ୍ତୁ ଉପରେ ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ବଳ (F) ପ୍ରୟୋଗ କରାଯାଏ ଏବଂ ବଳର ଦିଗରେ ବସ୍ତୁର ବିସ୍ଥାପନ (s) ଘଟେ, ସେତେବେଳେ ସମ୍ପାଦିତ କାର୍ଯ୍ୟ (W) ହେଉଛି ବଳ ଓ ବିସ୍ଥାପନର ଗୁଣଫଳ ।
ସୂତ୍ର: କାର୍ଯ୍ୟ = ବଳ × ବିସ୍ଥାପନ
W = F × s
ଉଦାହରଣ : ୮.୧ (ପାଠ୍ୟପୁସ୍ତକରୁ)
୫ ନିଉଟନ ବଳ ଏକ ବସ୍ତୁକୁ ବଳ ଦିଗରେ ୨ ମିଟର ବିସ୍ଥାପିତ କରାଇଲେ, ସମ୍ପାଦିତ କାର୍ଯ୍ୟର ପରିମାଣ କେତେ ?
ଉତ୍ତର:
ବଳ, F = ୫ ନିଉଟନ
ବିସ୍ଥାପନ, s = ୨ ମିଟର
ସମ୍ପାଦିତ କାର୍ଯ୍ୟ, W = F × s
W = ୫ ନିଉଟନ × ୨ ମିଟର = ୧୦ ଜୁଲ୍
ଉଦାହରଣ : ୮.୨ (ପାଠ୍ୟପୁସ୍ତକରୁ)
ଜଣେ କୁଲି ୧୫ କିଗ୍ରା ଓଜନର ଏକ ବ୍ୟାଗକୁ ତଳୁ ୧.୫ ମିଟର ଉଠାଇ ନିଜ ମୁଣ୍ଡ ଉପରେ ରଖିଲା । ଏଠାରେ କୁଲିଦ୍ୱାରା ସମ୍ପାଦିତ ହୋଇଥିବା କାର୍ଯ୍ୟର ପରିମାଣ କେତେ ? (g = 10 ମି/ସେ²)
ଉତ୍ତର:
ବ୍ୟାଗର ବସ୍ତୁତ୍ଵ, m = ୧୫ କିଗ୍ରା
ବ୍ୟାଗର ବିସ୍ଥାପନ, s = ୧.୫ ମି
ବ୍ୟାଗର ଓଜନ = mg (ଏହା ଏକ ବଳ ଯାହା କୁଲି ପ୍ରୟୋଗ କରୁଛି)
W = F × s
W = mg × s
W = ୧୫ କିଗ୍ରା × ୧୦ ମି/ସେ² × ୧.୫ ମି
W = ୨୨୫ ନିଉଟନ × ମିଟର
W = ୨୨୫ ଜୁଲ୍
ଅତଏବ କୁଲିଟି ୨୨୫ ଜୁଲ୍ କାର୍ଯ୍ୟ କରିଛି ।
୨.୨ ଶକ୍ତି (Energy)
୨.୨.୧ ଶକ୍ତିର ସଂଜ୍ଞା (Definition of Energy):
କାର୍ଯ୍ୟ କରିବାର ସାମର୍ଥ୍ୟକୁ ଶକ୍ତି କୁହାଯାଏ । ଯେଉଁ ବସ୍ତୁର କାର୍ଯ୍ୟ କରିବାପାଇଁ କ୍ଷମତା ଥାଏ, ତାହା ମଧ୍ୟରେ ଶକ୍ତି ରହିଥାଏ ।
୨.୨.୨ ଶକ୍ତିର ପ୍ରକାରଭେଦ (Forms of Energy):
ଶକ୍ତି ବିଭିନ୍ନ ରୂପରେ ଦେଖାଦେଇଥାଏ । ସେଗୁଡ଼ିକ ହେଲା:
୨.୨.୩ ଗତିଜ ଶକ୍ତି (Kinetic Energy):
ମନେକର, 'm' ବସ୍ତୁତ୍ଵ ବିଶିଷ୍ଟ ଏକ ବସ୍ତୁ 'u' ପ୍ରାରମ୍ଭିକ ବେଗରେ ଗତି କରୁଛି । ଏହି ବସ୍ତୁ ଉପରେ ତାର ଗତିର ଦିଗରେ 'F' ବଳ ପ୍ରୟୋଗ କରାଗଲା । ଏହା ଯୋଗୁଁ ବସ୍ତୁରେ 'a' ତ୍ୱରଣ ସୃଷ୍ଟି ହେଲା ଓ ବସ୍ତୁର ବେଗ ବୃଦ୍ଧି ପାଇଲା । 's' ଦୂରତା ଅତିକ୍ରମ କଲାପରେ ତା’ର ବେଗ 'v' ହେଲା ।
ତ୍ୱରାନ୍ୱିତ ଗତିର ତୃତୀୟ ସମୀକରଣ ଅନୁସାରେ:
v² = u² + 2as
ଏଥିରୁ, 2as = v² - u²
s = (v² - u²) / (2a) ...........(i)
ଆମେ ଜାଣୁ, ବଳ F = ma
ସମ୍ପାଦିତ କାର୍ଯ୍ୟ W = F × s
W = ma × [(v² - u²) / (2a)]
W = (m/2) × (v² - u²)
W = (1/2)mv² - (1/2)mu²
ଯଦି ପ୍ରାରମ୍ଭରୁ ବସ୍ତୁ ସ୍ଥିର ରହିଥାଏ, ତେବେ ତାହାର ପ୍ରାରମ୍ଭିକ ବେଗ u = 0 ହୁଏ ।
ତେଣୁ, W = (1/2)mv²
ଏହି କାର୍ଯ୍ୟ ବସ୍ତୁରେ ଗତିଜ ଶକ୍ତି (E_k) ରୂପରେ ଗଚ୍ଛିତ ରହେ ।
ଅତଏବ, E_k = (1/2)mv²
ଉଦାହରଣ : ୮.୩ (ପାଠ୍ୟପୁସ୍ତକରୁ)
୧୫ କିଗ୍ରା ବସ୍ତୁତ୍ଵ ବିଶିଷ୍ଟ ଏକ ବସ୍ତୁ ୪ ମି/ସେ ପରିବେଗରେ ଗତି କରୁଛି । ବସ୍ତୁର ଗତିଜ ଶକ୍ତି କେତେ ?
ଉତ୍ତର:
ବସ୍ତୁର ବସ୍ତୁତ୍ଵ, m = ୧୫ କିଗ୍ରା
ବସ୍ତୁର ପରିବେଗ, v = ୪ ମି/ସେ
ଗତିଜ ଶକ୍ତି, E_k = (1/2)mv²
E_k = (1/2) × ୧୫ କିଗ୍ରା × (୪ ମି/ସେ)²
E_k = (1/2) × ୧୫ କିଗ୍ରା × ୧୬ ମି²/ସେ²
E_k = ୧୫ × ୮ ଜୁଲ୍
E_k = ୧୨୦ ଜୁଲ୍
ଅତଏବ ବସ୍ତୁଟିର ଗତିଜ ଶକ୍ତି ୧୨୦ ଜୁଲ୍ ଅଟେ ।
ଉଦାହରଣ : ୮.୪ (ପାଠ୍ୟପୁସ୍ତକରୁ)
୧୫୦୦ କିଗ୍ରା ଓଜନର ଏକ ମୋଟର କାର୍ର ବେଗ ୩୦ କିମି/ଘଣ୍ଟାରୁ ୬୦ କିମି/ଘଣ୍ଟାକୁ ବୃଦ୍ଧି ପାଇଲେ, କେତେ ପରିମାଣର କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହୁଏ ?
ଉତ୍ତର:
ମୋଟର କାର୍ର ବସ୍ତୁତ୍ଵ, m = ୧୫୦୦ କିଗ୍ରା
କାର୍ର ପ୍ରାରମ୍ଭିକ ବେଗ, u = ୩୦ କିମି/ଘଣ୍ଟା
u = ୩୦ × (୫/୧୮) ମି/ସେ = ୮.୩୩ ମି/ସେ (ପ୍ରାୟ)
କାର୍ର ଅନ୍ତିମ ବେଗ, v = ୬୦ କିମି/ଘଣ୍ଟା
v = ୬୦ × (୫/୧୮) ମି/ସେ = ୧୬.୬୭ ମି/ସେ (ପ୍ରାୟ)
ପ୍ରାରମ୍ଭିକ ଗତିଜ ଶକ୍ତି, E_ki = (1/2)mu²
E_ki = (1/2) × ୧୫୦୦ କିଗ୍ରା × (୮.୩୩ ମି/ସେ)²
E_ki = (1/2) × ୧୫୦୦ × ୬୯.୩୮୮୯ ଜୁଲ୍
E_ki = ୭୫୦ × ୬୯.୩୮୮୯ ଜୁଲ୍
E_ki = ୫୨୦୪୧.୬୮ ଜୁଲ୍ (ପ୍ରାୟ)
ଅନ୍ତିମ ଗତିଜ ଶକ୍ତି, E_kf = (1/2)mv²
E_kf = (1/2) × ୧୫୦୦ କିଗ୍ରା × (୧୬.୬୭ ମି/ସେ)²
E_kf = (1/2) × ୧୫୦୦ × ୨୭୭.୮୮୮୯ ଜୁଲ୍
E_kf = ୭୫୦ × ୨୭୭.୮୮୮୯ ଜୁଲ୍
E_kf = ୨୦୮୪୧୬.୬୮ ଜୁଲ୍ (ପ୍ରାୟ)
ସମ୍ପାଦିତ କାର୍ଯ୍ୟର ପରିମାଣ = ଗତିଜ ଶକ୍ତିର ପରିବର୍ତ୍ତନ
W = E_kf - E_ki
W = ୨୦୮୪୧୬.୬୮ ଜୁଲ୍ - ୫୨୦୪୧.୬୮ ଜୁଲ୍
W = ୧୫୬୩୭୫ ଜୁଲ୍
୨.୨.୪ ସ୍ଥିତିଜ ଶକ୍ତି (Potential Energy):
ମନେକର 'm' ବସ୍ତୁତ୍ଵ ବିଶିଷ୍ଟ ଏକ ବସ୍ତୁକୁ ଭୂପୃଷ୍ଠରୁ 'h' ଉଚ୍ଚତା ପର୍ଯ୍ୟନ୍ତ ଉଠାଗଲା । ଏହି ଉଚ୍ଚତା ପର୍ଯ୍ୟନ୍ତ ଉଠାଇବା ପାଇଁ ଆବଶ୍ୟକ ନ୍ୟୁନତମ ବଳ ବସ୍ତୁର ଓଜନ (mg) ସହିତ ସମାନ ।
ଅତଏବ, F = mg
ବିସ୍ଥାପନ, s = h
ସମ୍ପାଦିତ କାର୍ଯ୍ୟ, W = F × s
W = mg × h
ଏହି କାର୍ଯ୍ୟ ବସ୍ତୁରେ ସ୍ଥିତିଜ ଶକ୍ତି (E_p) ରୂପରେ ଗଚ୍ଛିତ ରହେ ।
ଅତଏବ, E_p = mgh
ଉଦାହରଣ : ୮.୫ (ପାଠ୍ୟପୁସ୍ତକରୁ)
ଭୂମିଠାରୁ ୬ ମିଟର ଉଚ୍ଚତାରେ ଥିବା ୧୦ କିଗ୍ରା ବସ୍ତୁତ୍ଵ ବିଶିଷ୍ଟ ଗୋଟିଏ ବସ୍ତୁର ସ୍ଥିତିଜ ଶକ୍ତି କେତେ କଳନା କର । (g = ୯.୮ ମି/ସେ²)
ଉତ୍ତର:
ବସ୍ତୁର ବସ୍ତୁତ୍ଵ, m = ୧୦ କିଗ୍ରା
ବସ୍ତୁର ଉଚ୍ଚତା, h = ୬ ମି
ମାଧ୍ୟାକର୍ଷଣଜନିତ ତ୍ୱରଣ, g = ୯.୮ ମି/ସେ²
ସ୍ଥିତିଜ ଶକ୍ତି, E_p = mgh
E_p = ୧୦ କିଗ୍ରା × ୯.୮ ମି/ସେ² × ୬ ମି
E_p = ୯୮ ନିଉଟନ × ୬ ମି
E_p = ୫୮୮ ଜୁଲ୍
ଅତଏବ ବସ୍ତୁଟିର ସ୍ଥିତିଜ ଶକ୍ତି ୫୮୮ ଜୁଲ୍ ହେବ ।
ଉଦାହରଣ : ୮.୬ (ପାଠ୍ୟପୁସ୍ତକରୁ)
୧୨ କିଗ୍ରା ଓଜନ ବିଶିଷ୍ଟ ଗୋଟିଏ ବସ୍ତୁକୁ ଭୂମି ଉପରୁ କିଛି ଉଚ୍ଚତାକୁ ଉଠାଯାଇଛି । ଯଦି ସେହି ଉଚ୍ଚତାରେ ବସ୍ତୁଟିର ସ୍ଥିତିଜ ଶକ୍ତି ୪୮୦ ଜୁଲ୍ ହୁଏ ତେବେ ବସ୍ତୁଟି ଭୂପୃଷ୍ଠରୁ କେତେ ଉଚ୍ଚରେ ଅଛି ନିର୍ଣ୍ଣୟ କର । (g = ୧୦ ମି/ସେ²)
ଉତ୍ତର:
ବସ୍ତୁର ବସ୍ତୁତ୍ଵ, m = ୧୨ କିଗ୍ରା
ସ୍ଥିତିଜ ଶକ୍ତି, E_p = ୪୮୦ ଜୁଲ୍
ମାଧ୍ୟାକର୍ଷଣଜନିତ ତ୍ୱରଣ, g = ୧୦ ମି/ସେ²
ଆମେ ଜାଣୁ, E_p = mgh
h = E_p / (mg)
h = ୪୮୦ ଜୁଲ୍ / (୧୨ କିଗ୍ରା × ୧୦ ମି/ସେ²)
h = ୪୮୦ ଜୁଲ୍ / ୧୨୦ ନିଉଟନ
h = ୪ ମିଟର
ଅତଏବ ବସ୍ତୁଟି ଭୂମି ଉପରୁ ୪ ମିଟର ଉଚ୍ଚତାରେ ଅଛି ।
୨.୨.୫ ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମ (Law of Conservation of Energy):
୨.୩ କ୍ଷମତା (Power)
୨.୩.୧ କ୍ଷମତାର ସଂଜ୍ଞା (Definition of Power):
କାର୍ଯ୍ୟ କରିବାର ହାରକୁ ବା ଶକ୍ତି ବିନିଯୋଗର ହାରକୁ କ୍ଷମତା କୁହାଯାଏ । ଏହା କୌଣସି କାରକ କେତେ ଶୀଘ୍ର ବା କେତେ ଧୀର ଭାବେ କାର୍ଯ୍ୟ ସମ୍ପାଦନ କରୁଛି ତାହା ଦର୍ଶାଏ ।
ଉଦାହରଣ : ୮.୭ (ପାଠ୍ୟପୁସ୍ତକରୁ)
A ଓ B ନାମକ ଦୁଇଜଣ ବାଳିକା ଏକ ଦଉଡ଼ିକୁ ଧରି ପୃଥକ ପୃଥକ ଭାବେ ୮ ମି ଉଚ୍ଚତା ପର୍ଯ୍ୟନ୍ତ ଚଢ଼ିଗଲେ । ପ୍ରତ୍ୟେକଙ୍କର ଓଜନ ୪୦୦ ନିଉଟନ । ଯଦି ଏହି କାମପାଇଁ A ନାମଧାରୀ ବାଳିକାକୁ ୨୦ ସେକେଣ୍ଡ ଏବଂ B ନାମଧାରୀ ବାଳିକାକୁ ୫୦ ସେକେଣ୍ଡ ସମୟ ଲାଗିଲା, ତେବେ ପ୍ରତ୍ୟେକ ବାଳିକାଙ୍କର ପାଓ୍ବାର ନିର୍ଣ୍ଣୟ କର ।
ଉତ୍ତର:
(i) A ବାଳିକାର ପାଓ୍ବାର ନିର୍ଣ୍ଣୟ:
A ବାଳିକାର ଓଜନ, mg = ୪୦୦ ନିଉଟନ
ବିସ୍ଥାପନ (ଉଚ୍ଚତା), h = ୮ ମି
ସମୟ, t = ୨୦ ସେ
ପାଓ୍ବାର, P = (କାର୍ଯ୍ୟ / ସମୟ) = (mgh / t)
P = (୪୦୦ ନିଉଟନ × ୮ ମି) / ୨୦ ସେ
P = ୩୨୦୦ ଜୁଲ୍ / ୨୦ ସେ
P = ୧୬୦ ୱାଟ୍
(ii) B ବାଳିକାର ପାଓ୍ବାର ନିର୍ଣ୍ଣୟ:
B ବାଳିକାର ଓଜନ, mg = ୪୦୦ ନିଉଟନ
ବିସ୍ଥାପନ (ଉଚ୍ଚତା), h = ୮ ମି
ସମୟ, t = ୫୦ ସେ
ପାଓ୍ବାର, P = (କାର୍ଯ୍ୟ / ସମୟ) = (mgh / t)
P = (୪୦୦ ନିଉଟନ × ୮ ମି) / ୫୦ ସେ
P = ୩୨୦୦ ଜୁଲ୍ / ୫୦ ସେ
P = ୬୪ ୱାଟ୍
ଅତଏବ A ବାଳିକାର ପାଓ୍ବାର ୧୬୦ ୱାଟ୍ ଓ B ବାଳିକାର ପାଓ୍ବାର ୬୪ ୱାଟ୍ ଅଟେ ।
ଉଦାହରଣ : ୮.୮ (ପାଠ୍ୟପୁସ୍ତକରୁ)
୫୦ କିଗ୍ରା ଓଜନ ବିଶିଷ୍ଟ ଜଣେ ବାଳକ ୯ ସେକେଣ୍ଡ ସମୟ ମଧ୍ୟରେ ୪୫ ପାହାଚ ବିଶିଷ୍ଟ ଏକ ଶିଡ଼ିଘରକୁ ଚଢ଼ିପାରେ । ଯଦି ପ୍ରତ୍ୟେକ ପାହାଚର ଉଚ୍ଚତା ୧୫ ସେମି ହୁଏ, ତେବେ ବାଳକଟିର ପାଓ୍ବାର ନିର୍ଣ୍ଣୟ କର । (g = ୧୦ ମି/ସେ²)
ଉତ୍ତର:
ବାଳକଟିର ବସ୍ତୁତ୍ଵ, m = ୫୦ କିଗ୍ରା
ବାଳକଟିର ଓଜନ, mg = ୫୦ କିଗ୍ରା × ୧୦ ମି/ସେ² = ୫୦୦ ନିଉଟନ
ଶିଡ଼ିର ମୋଟ ଉଚ୍ଚତା, h = ୪୫ × ୧୫ ସେମି
h = ୪୫ × (୧୫/୧୦୦) ମିଟର
h = ୪୫ × ୦.୧୫ ମିଟର
h = ୬.୭୫ ମିଟର
ଶିଡ଼ି ଚଢ଼ିବା ପାଇଁ ସମୟ, t = ୯ ସେ
ପାଓ୍ବାର, P = (କାର୍ଯ୍ୟ / ସମୟ) = (mgh / t)
P = (୫୦୦ ନିଉଟନ × ୬.୭୫ ମି) / ୯ ସେ
P = ୩୩୭୫ ଜୁଲ୍ / ୯ ସେ
P = ୩୭୫ ୱାଟ୍
ଅତଏବ ବାଳକଟିର ପାଓ୍ବାର ୩୭୫ ୱାଟ୍ ।
୨.୪ ଶକ୍ତିର ବ୍ୟବସାୟିକ ଏକକ (Commercial Unit of Energy):
ଉଦାହରଣ : ୮.୯ (ପାଠ୍ୟପୁସ୍ତକରୁ)
ଗୋଟିଏ ୬୦ ୱାଟର ବଲ୍ବ ପ୍ରତିଦିନ ୬ ଘଣ୍ଟା ଲେଖାଁଏ ଜଳିଲେ କେତେ ପରିମାଣର ଶକ୍ତି ଗୋଟିଏ ଦିନରେ ଖର୍ଚ୍ଚ ହେବ ?
ଉତ୍ତର:
ବିଦ୍ୟୁତ୍ ବଲ୍ବର ପାଓ୍ବାର, P = ୬୦ ୱାଟ୍ = ୦.୦୬ କିଲୋୱାଟ୍
ଦୈନିକ ଜଳିବା ସମୟ, t = ୬ ଘଣ୍ଟା
ବ୍ୟବହୃତ ଶକ୍ତିର ପରିମାଣ = ପାଓ୍ବାର × ସମୟ
E = P × t
E = ୦.୦୬ କିଲୋୱାଟ୍ × ୬ ଘଣ୍ଟା
E = ୦.୩୬ କିଲୋୱାଟ ଘଣ୍ଟା
E = ୦.୩୬ ୟୁନିଟ୍
ଅତଏବ ବିଦ୍ୟୁତ୍ ବଲ୍ବଟି ଦିନକୁ ୦.୩୬ ୟୁନିଟ୍ର ଶକ୍ତି ଖର୍ଚ୍ଚ କରିବ ।
୩. ପାଠ୍ୟପୁସ୍ତକ ଅଭ୍ୟାସ ପ୍ରଶ୍ନାବଳୀର ୧୦୦% ସମ୍ପୂର୍ଣ୍ଣ ସମାଧାନ (100% Complete Solved Exercises)
୩.୧ ଅଧ୍ୟାୟ ମଧ୍ୟବର୍ତ୍ତୀ ପ୍ରଶ୍ନଗୁଡ଼ିକର ସମାଧାନ (In-Chapter Questions)
Q1. ଆମେ କେଉଁ କ୍ଷେତ୍ରରେ କହିବା ଯେ କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହୋଇଛି ?
ଉତ୍ତର: ବିଜ୍ଞାନ ଅନୁଯାୟୀ, କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହେବା ପାଇଁ ନିମ୍ନଲିଖିତ ଦୁଇଟି ସର୍ତ୍ତ ପୂରଣ ହେବା ଆବଶ୍ୟକ:
୧. ବସ୍ତୁ ଉପରେ ବଳ ପ୍ରୟୋଗ ହେବା ଆବଶ୍ୟକ ।
୨. ବଳ ପ୍ରୟୋଗ ହେବା ଦ୍ୱାରା ବସ୍ତୁର ବିସ୍ଥାପନ ଘଟିବା ଆବଶ୍ୟକ ।
ଯେଉଁ କ୍ଷେତ୍ରରେ ଏହି ଦୁଇଟି ସର୍ତ୍ତ ପୂରଣ ହୁଏ, ସେଠାରେ କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହୋଇଛି ବୋଲି କୁହାଯାଏ ।
Q2. କାର୍ଯ୍ୟର ଏକ ଉଦାହରଣ ଦିଅ ଯେଉଁଠାରେ କି ବସ୍ତୁ ଉପରେ ପ୍ରୟୋଗ ହୋଇଥିବା ବଳ ଏବଂ ଏହାଦ୍ୱାରା ବସ୍ତୁର ବିସ୍ଥାପନ ଏକ ଦିଗରେ ହୋଇଥିବ ।
ଉତ୍ତର: ଯେତେବେଳେ ଜଣେ ବ୍ୟକ୍ତି ଏକ ଟ୍ରଲିକୁ ଟାଣେ, ଟଣାବଳର ଦିଗରେ ଟ୍ରଲିଟି ଗତି କରେ । ଏଠାରେ ଟଣାବଳ ଓ ଟ୍ରଲିର ବିସ୍ଥାପନ ଏକ ଦିଗରେ ଥିବାରୁ କାର୍ଯ୍ୟ ଯୁକ୍ତାତ୍ମକ ଅଟେ ।
Q3. କାର୍ଯ୍ୟର ଆଉ ଏକ ଉଦାହରଣ ଦିଅ ଯେଉଁ କ୍ଷେତ୍ରରେ ବସ୍ତୁ ଉପରେ ପ୍ରୟୋଗ ହୋଇଥିବା ବଳ ଏବଂ ବସ୍ତୁର ବିସ୍ଥାପନ ବିପରୀତ ଦିଗରେ ହୋଇଥିବ ।
ଉତ୍ତର: ଯେତେବେଳେ ଜଣେ ବ୍ୟକ୍ତି ପାହାଡ଼ ଉପରକୁ ଚଢ଼େ, ସେତେବେଳେ ବ୍ୟକ୍ତିର ବିସ୍ଥାପନ ଉପର ଦିଗରେ ହୁଏ କିନ୍ତୁ ମାଧ୍ୟାକର୍ଷଣ ବଳ ତଳ ଦିଗରେ କାର୍ଯ୍ୟ କରେ । ଏଠାରେ ବଳ ଓ ବିସ୍ଥାପନ ବିପରୀତ ଦିଗରେ ଥିବାରୁ ସମ୍ପାଦିତ କାର୍ଯ୍ୟ ବିଯୁକ୍ତାତ୍ମକ ଅଟେ ।
Q4. ଏକ ଜୁଲ୍ କାର୍ଯ୍ୟକୁ ଗାଣିତିକ ଭାଷାରେ ପ୍ରକାଶ କର ।
ଉତ୍ତର: ଏକ ଜୁଲ୍ କାର୍ଯ୍ୟକୁ ଗାଣିତିକ ଭାଷାରେ ନିମ୍ନଲିଖିତ ଭାବରେ ପ୍ରକାଶ କରାଯାଏ:
1 ଜୁଲ୍ = 1 ନିଉଟନ × 1 ମିଟର
ଅର୍ଥାତ୍, ଯଦି ଏକ ନିଉଟନ (1 N) ବଳ ଏକ ବସ୍ତୁ ଉପରେ କାର୍ଯ୍ୟକରି ବସ୍ତୁକୁ ବଳ ଦିଗରେ ଏକ ମିଟର (1 m) ବିସ୍ଥାପିତ କରେ, ତେବେ ବଳ ଦ୍ୱାରା ସମ୍ପାଦିତ କାର୍ଯ୍ୟକୁ ଏକ ଜୁଲ୍ କୁହାଯାଏ ।
Q1. କୌଣସି ବସ୍ତୁର ଗତିଜ ଶକ୍ତି କ’ଣ ?
ଉତ୍ତର: ଗୋଟିଏ ବସ୍ତୁ ତାହାର ଗତି ଯୋଗୁଁ ଯେଉଁ ଶକ୍ତି ଆହରଣ କରିଥାଏ, ତାହାକୁ ବସ୍ତୁର ଗତିଜ ଶକ୍ତି କୁହାଯାଏ । ଗତିଶୀଳ ବସ୍ତୁରେ ଗତିଜ ଶକ୍ତି ଥାଏ ।
Q2. ବସ୍ତୁର ଗତିଜ ଶକ୍ତିର ସମୀକରଣ ଲେଖ ?
ଉତ୍ତର: ଯଦି 'm' ବସ୍ତୁତ୍ଵ ବିଶିଷ୍ଟ ଏକ ବସ୍ତୁ 'v' ପରିବେଗରେ ଗତି କରୁଥାଏ, ତେବେ ତାହାର ଗତିଜ ଶକ୍ତି (E_k) ନିମ୍ନଲିଖିତ ସମୀକରଣ ଦ୍ୱାରା ପ୍ରକାଶ କରାଯାଏ:
E_k = (1/2)mv²
Q3. ଗୋଟିଏ ବସ୍ତୁର ବସ୍ତୁତ୍ଵ m, ପରିବେଗ 5 ମି/ସେ ଏବଂ ଗତିଜ ଶକ୍ତି 25 ଜୁଲ୍ । ଯଦି ବସ୍ତୁର ପରିବେଗକୁ ଦ୍ୱିଗୁଣିତ କରାଯାଏ, ତେବେ ତାହାର ଗତିଜଶକ୍ତି କେତେ ହେବ ? ଗତିଜ ଶକ୍ତି କେତେ ଗୁଣ ହୋଇଗଲା ?
ଉତ୍ତର:
ପ୍ରାରମ୍ଭିକ ଅବସ୍ଥା:
ବସ୍ତୁତ୍ଵ = m
ପରିବେଗ, v₁ = 5 ମି/ସେ
ଗତିଜ ଶକ୍ତି, E_k₁ = 25 ଜୁଲ୍
ସୂତ୍ର ଅନୁଯାୟୀ, E_k₁ = (1/2)mv₁²
25 = (1/2)m(5)²
25 = (1/2)m(25)
m = (25 × 2) / 25
m = 2 କିଗ୍ରା
ଦ୍ୱିତୀୟ ଅବସ୍ଥା:
ବସ୍ତୁତ୍ଵ = m = 2 କିଗ୍ରା
ପରିବେଗକୁ ଦ୍ୱିଗୁଣିତ କରାଗଲା, v₂ = 2 × v₁ = 2 × 5 ମି/ସେ = 10 ମି/ସେ
ନୂତନ ଗତିଜ ଶକ୍ତି, E_k₂ = (1/2)mv₂²
E_k₂ = (1/2) × 2 କିଗ୍ରା × (10 ମି/ସେ)²
E_k₂ = 1 × 100 ଜୁଲ୍
E_k₂ = 100 ଜୁଲ୍
ଗତିଜ ଶକ୍ତି କେତେ ଗୁଣ ହୋଇଗଲା:
E_k₂ / E_k₁ = 100 ଜୁଲ୍ / 25 ଜୁଲ୍ = 4
ଅତଏବ, ବସ୍ତୁର ପରିବେଗକୁ ଦ୍ୱିଗୁଣିତ କଲେ ତାହାର ଗତିଜ ଶକ୍ତି ୧୦୦ ଜୁଲ୍ ହେବ ଏବଂ ଏହା ପ୍ରାରମ୍ଭିକ ଗତିଜ ଶକ୍ତିର ୪ ଗୁଣ ହୋଇଯିବ ।
Q1. ପାଓ୍ବାରର ସଂଜ୍ଞା କ’ଣ ?
ଉତ୍ତର: କାର୍ଯ୍ୟ କରିବାର ହାରକୁ ବା ଶକ୍ତି ବିନିଯୋଗର ହାରକୁ କ୍ଷମତା (ପାଓ୍ବାର) କୁହାଯାଏ । ଏହା କୌଣସି କାରକ କେତେ ଶୀଘ୍ର ବା କେତେ ଧୀର ଭାବେ କାର୍ଯ୍ୟ ସମ୍ପାଦନ କରୁଛି ତାହା ଦର୍ଶାଏ ।
Q2. ଏକ ୱାଟ୍ ପାଓ୍ବାର କହିଲେ କ’ଣ ବୁଝ ?
ଉତ୍ତର: ଯଦି ଗୋଟିଏ କାରକ ଏକ ସେକେଣ୍ଡରେ ଏକ ଜୁଲ୍ କାର୍ଯ୍ୟ ସମ୍ପାଦନ କରିପାରେ, ତେବେ ତାହାର କ୍ଷମତାକୁ ଏକ ୱାଟ୍ କୁହାଯାଏ ।
1 ୱାଟ୍ = 1 ଜୁଲ୍ / 1 ସେକେଣ୍ଡ
Q3. ଗୋଟିଏ ବିଦ୍ୟୁତ୍ ବଲ୍ବ 10 ସେକେଣ୍ଡ ସମୟ ମଧ୍ୟରେ 1000 ଜୁଲ୍ ଶକ୍ତି ବ୍ୟବହାର କରେ । ତେବେ ତାହାର ପାଓ୍ବାର କେତେ ?
ଉତ୍ତର:
ବ୍ୟବହୃତ ଶକ୍ତି, W = 1000 ଜୁଲ୍
ସମୟ, t = 10 ସେକେଣ୍ଡ
ପାଓ୍ବାର, P = W / t
P = 1000 ଜୁଲ୍ / 10 ସେକେଣ୍ଡ
P = 100 ୱାଟ୍
ଅତଏବ ବିଦ୍ୟୁତ୍ ବଲ୍ବର ପାଓ୍ବାର ୧୦୦ ୱାଟ୍ ।
Q4. ହାରାହାରି ପାଓ୍ବାର କେତେବେଳେ ନିର୍ଣ୍ଣୟ କରାଯାଏ । ଏହାର ସଂଜ୍ଞା କ’ଣ ?
ଉତ୍ତର: ଯେତେବେଳେ କାର୍ଯ୍ୟ କରିବାର ହାର ସମୟାନୁସାରେ ବଦଳିପାରେ, ଅର୍ଥାତ୍ ଗୋଟିଏ ବସ୍ତୁ ଅଲଗା ଅଲଗା ସମୟ ବ୍ୟବଧାନରେ ଅଲଗା ଅଲଗା ହାରରେ କାର୍ଯ୍ୟ ସମ୍ପାଦନ କରେ, ସେତେବେଳେ ହାରାହାରି ପାଓ୍ବାର ନିର୍ଣ୍ଣୟ କରାଯାଏ ।
ସଂଜ୍ଞା: କାର୍ଯ୍ୟ ସମ୍ପାଦନ ସମୟରେ ମୋଟ ସମ୍ପାଦିତ କାର୍ଯ୍ୟ ଏବଂ ମୋଟ ସମୟର ଅନୁପାତକୁ ହାରାହାରି ପାଓ୍ବାର କୁହାଯାଏ ।
ହାରାହାରି ପାଓ୍ବାର = ମୋଟ ସମ୍ପାଦିତ କାର୍ଯ୍ୟ / ମୋଟ ସମୟ
୩.୨ ତୁମ ପାଇଁ କାମ (Activities) ର ସମାଧାନ
ତୁମ ପାଇଁ କାମ : ୮.୧ (ପୃଷ୍ଠା ୨)
ତୁମର ଦୈନନ୍ଦିନ ଜୀବନରେ କାର୍ଯ୍ୟକରିବାର କିଛି ଉଦାହରଣକୁ ମନେ ପକାଅ ଓ ତା’ର ଏକ ତାଲିକା ପ୍ରସ୍ତୁତ କର । ଏପରି ଉଦାହରଣଗୁଡ଼ିକୁ ତୁମ ସାଙ୍ଗମାନଙ୍କ ସହିତ ଆଲୋଚନା କର ଏବଂ ପ୍ରତ୍ୟେକଟି କ୍ଷେତ୍ରରେ କାର୍ଯ୍ୟ ହୋଇଛିକି ନାହିଁ ସେ ବିଷୟରେ ଚିନ୍ତା କର । ଏପରି କିଛି ଉଦାହରଣ ଦିଅ ଯେଉଁଠାରେ କି ବଳପ୍ରୟୋଗ ହୋଇ ମଧ୍ୟ ବସ୍ତୁଟିର ଅବସ୍ଥାନରେ କୌଣସି ପରିବର୍ତ୍ତନ ହୋଇନାହିଁ । ଏପରି ପରିସ୍ଥିତି ବିଷୟରେ ଚିନ୍ତାକର ଯେଉଁଠାରେ କି କୌଣସି ବଳ ପ୍ରୟୋଗ ନହୋଇ ମଧ୍ୟ ବସ୍ତୁଟି ବିସ୍ଥାପିତ ହୋଇପାରିଛି ।
ଉତ୍ତର:
କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହେଉଥିବା ଉଦାହରଣ:
୧. ଏକ ବହିକୁ ଟେବୁଲ ଉପରୁ ଉଠାଇବା । (ବଳ ପ୍ରୟୋଗ ହେଉଛି ଓ ବହିର ବିସ୍ଥାପନ ଘଟୁଛି)
୨. ଏକ ଫୁଟବଲକୁ ଗୋଇଠା ମାରିବା । (ବଳ ପ୍ରୟୋଗ ହେଉଛି ଓ ଫୁଟବଲର ବିସ୍ଥାପନ ଘଟୁଛି)
୩. ଏକ ଟ୍ରଲିକୁ ଟାଣିବା । (ବଳ ପ୍ରୟୋଗ ହେଉଛି ଓ ଟ୍ରଲିର ବିସ୍ଥାପନ ଘଟୁଛି)
କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ନହେଉଥିବା ଉଦାହରଣ (ବଳ ପ୍ରୟୋଗ ହୋଇ ମଧ୍ୟ ବିସ୍ଥାପନ ନାହିଁ):
୧. ଏକ କାନ୍ଥକୁ ଠେଲିବା । (ବଳ ପ୍ରୟୋଗ ହେଉଛି କିନ୍ତୁ କାନ୍ଥର ବିସ୍ଥାପନ ନାହିଁ)
୨. ଏକ ବଡ଼ ପଥରକୁ ଠେଲିବା । (ବଳ ପ୍ରୟୋଗ ହେଉଛି କିନ୍ତୁ ପଥରର ବିସ୍ଥାପନ ନାହିଁ)
୩. ମୁଣ୍ଡରେ ବୋଝ ମୁଣ୍ଡେଇ ଠିଆ ହୋଇ ରହିବା । (ବଳ ପ୍ରୟୋଗ ହେଉଛି କିନ୍ତୁ ବସ୍ତୁର ବିସ୍ଥାପନ ନାହିଁ)
ବଳ ପ୍ରୟୋଗ ନହୋଇ ମଧ୍ୟ ବସ୍ତୁ ବିସ୍ଥାପିତ ହୋଇପାରିଥିବା ପରିସ୍ଥିତି:
ଏପରି ପରିସ୍ଥିତି ସାଧାରଣତଃ ସମ୍ଭବ ନୁହେଁ ଯେଉଁଠାରେ କୌଣସି ବଳ ପ୍ରୟୋଗ ନହୋଇ ବସ୍ତୁ ବିସ୍ଥାପିତ ହୋଇପାରିବ । ଗତିର ପ୍ରଥମ ନିୟମ ଅନୁଯାୟୀ, ବାହ୍ୟ ବଳ ପ୍ରୟୋଗ ନହେଲେ ବସ୍ତୁଟି ଯେଉଁ ଅବସ୍ଥାରେ ଥାଏ ସେହି ଅବସ୍ଥାରେ ରହେ (ସ୍ଥିର ଥିଲେ ସ୍ଥିର ରହେ, ଗତିଶୀଳ ଥିଲେ ସମବେଗରେ ଗତି କରେ) । ତେଣୁ, ବିସ୍ଥାପନ ପାଇଁ ବଳ ଅପରିହାର୍ଯ୍ୟ ।
ତୁମ ପାଇଁ କାମ : ୮.୨ (ପୃଷ୍ଠା ୪)
ଉପର ଆଲୋଚନାରେ ଆମେ ମାତ୍ର କେତୋଟି ଶକ୍ତିର ଉତ୍ସ ବିଷୟରେ ସୂଚନା ଦେଇଛୁ । ଏହାଛଡ଼ା ଆହୁରି ଅନେକ ଶକ୍ତିର ଉତ୍ସ ରହିଛି । ତାହାର ଏକ ତାଲିକା ପ୍ରସ୍ତୁତ କର । ତୁମ ସାଙ୍ଗମାନଙ୍କ ମଧ୍ୟରେ ଛୋଟ ଛୋଟ ଗ୍ରୁପ୍ କରି କେଉଁ କେଉଁ ଶକ୍ତି ସୂର୍ଯ୍ୟଠାରୁ ମିଳିଥାଏ, ତାହା ଉପରେ ଆଲୋଚନା କର । ଏପରି କୌଣସି ଶକ୍ତି ରହିଛି, ଯାହାକି ସୂର୍ଯ୍ୟଠାରୁ ଆସି ନାହିଁ ? ତାହାର ଏକ ତାଲିକା କର ।
ଉତ୍ତର:
ଶକ୍ତିର ଉତ୍ସଗୁଡ଼ିକର ତାଲିକା:
୧. ସୂର୍ଯ୍ୟ (Solar Energy)
୨. ପବନ (Wind Energy)
୩. ଜଳ (Hydro Energy)
୪. ଜୀବାଶ୍ମ ଇନ୍ଧନ (Fossil Fuels - କୋଇଲା, ପେଟ୍ରୋଲିୟମ, ପ୍ରାକୃତିକ ଗ୍ୟାସ)
୫. ଜୈବ ବସ୍ତୁ (Biomass)
୬. ଭୂତାପ ଶକ୍ତି (Geothermal Energy)
୭. ପରମାଣୁ ଶକ୍ତି (Nuclear Energy)
୮. ଜୁଆର ଶକ୍ତି (Tidal Energy)
ସୂର୍ଯ୍ୟଠାରୁ ମିଳୁଥିବା ଶକ୍ତି:
ସୂର୍ଯ୍ୟଠାରୁ ନଆସୁଥିବା ଶକ୍ତି:
ତୁମ ପାଇଁ କାମ : ୮.୩ (ପୃଷ୍ଠା ୫)
ବାଲୁକା ଶଯ୍ୟା ଉପରେ ଏକ ଓଜନିଆ ବଲ୍କୁ ୨୫ ସେମି ଉଚ୍ଚତାରୁ ପକାଇ ବାଲି ଉପରେ ସୃଷ୍ଟି ହୋଇଥିବା ଅବତଳ ଆକାରର ଗାତର ଗଭୀରତାକୁ ମାପ । ଏହାପରେ ସେହି ବଲ୍କୁ ୫୦ ସେମି, ୧ ମିଟର ଓ ୫ ମିଟର ଉଚ୍ଚତାରୁ ପକାଇ ପ୍ରତିଥର ସୃଷ୍ଟି ହୋଇଥିବା ଅଲଗା ଅଲଗା ଅବତଳ ଗାତର ଗଭୀରତା ମାପ । ଗାତର ଗଭୀରତା ଓ ବଲ୍ ପଡ଼ୁଥିବା ଉଚ୍ଚତା ମଧ୍ୟରେ କି ସମ୍ପର୍କ ଅଛି ତାହା ଜାଣିବାକୁ ଚେଷ୍ଟା କର ।
ଉତ୍ତର:
ଏହି ପରୀକ୍ଷଣରୁ ଜଣାପଡ଼ିବ ଯେ, ବଲ୍କୁ ଯେତେ ଅଧିକ ଉଚ୍ଚତାରୁ ପକାଯାଏ, ବାଲି ଉପରେ ସୃଷ୍ଟି ହେଉଥିବା ଗାତର ଗଭୀରତା ସେତେ ଅଧିକ ହୁଏ ।
ସମ୍ପର୍କ: ବଲ୍ର ଉଚ୍ଚତା ବଢ଼ିଲେ ତାହାର ସ୍ଥିତିଜ ଶକ୍ତି (E_p = mgh) ବଢ଼େ । ଏହି ସ୍ଥିତିଜ ଶକ୍ତି ତଳକୁ ଖସିବା ସମୟରେ ଗତିଜ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ ହୁଏ । ବଲ୍ଟି ବାଲିରେ ପଡ଼ିବା ବେଳେ ଏହି ଗତିଜ ଶକ୍ତି ବାଲି ଉପରେ କାର୍ଯ୍ୟ କରି ଗାତ ସୃଷ୍ଟି କରେ । ଅଧିକ ଶକ୍ତି ଅଧିକ କାର୍ଯ୍ୟ କରିପାରେ, ତେଣୁ ଅଧିକ ଉଚ୍ଚତାରୁ ପଡ଼ିଲେ ଅଧିକ ଗଭୀର ଗାତ ସୃଷ୍ଟି ହୁଏ । ଏଥିରୁ ପ୍ରମାଣିତ ହୁଏ ଯେ ବସ୍ତୁର ସ୍ଥିତିଜ ଶକ୍ତି ତାହାର ଉଚ୍ଚତା ଉପରେ ନିର୍ଭର କରେ ।
ତୁମ ପାଇଁ କାମ : ୮.୬ (ପୃଷ୍ଠା ୯)
କିଛି ସାଙ୍ଗମାନଙ୍କୁ ନେଇ ଗୋଟିଏ ଛୋଟିଆ ଗ୍ରୁପ୍ (group)ରେ ବସ । ସମସ୍ତଙ୍କ ସାଙ୍ଗରେ ପ୍ରକୃତିରେ ହେଉଥିବା ବିଭିନ୍ନ ଶକ୍ତିର ରୂପାନ୍ତରଣ ବିଷୟରେ ଆଲୋଚନା କର । ସାଙ୍ଗମାନଙ୍କ ସହିତ ନିମ୍ନୋକ୍ତ ପ୍ରଶ୍ନଗୁଡ଼ିକ ବିଷୟରେ ଆଲୋଚନା କର ।
(କ) ସବୁଜ ଉଦ୍ଭିଦ କିପରି ଭାବେ ନିଜର ଖାଦ୍ୟ ପ୍ରସ୍ତୁତ କରନ୍ତି ?
(ଖ) ଏଥିପାଇଁ ସବୁଜ ଉଦ୍ଭିଦ କେଉଁଠୁ ଶକ୍ତି ପାଏ ?
(ଗ) ବାୟୁମଣ୍ଡଳରେ ବାୟୁ କିଭଳି ଭାବେ ଗୋଟିଏ ଜାଗାରୁ ଆଉ ଗୋଟିଏ ଜାଗାକୁ ଚଳପ୍ରଚଳ କରେ ?
(ଘ) କୋଇଲା, ପେଟ୍ରୋଲିୟମ ଭଳି ଇନ୍ଧନ ପ୍ରକୃତିରେ କିପରି ପ୍ରସ୍ତୁତ ହୁଏ ?
(ଙ) କେଉଁ ପ୍ରକାରର ଶକ୍ତି ରୂପାନ୍ତରଣ ଜଳଚକ୍ରକୁ ସାହାଯ୍ୟ କରିଥାଏ ?
ଉତ୍ତର:
(କ) ସବୁଜ ଉଦ୍ଭିଦ କିପରି ଭାବେ ନିଜର ଖାଦ୍ୟ ପ୍ରସ୍ତୁତ କରନ୍ତି ?
ସବୁଜ ଉଦ୍ଭିଦମାନେ ଆଲୋକ ସଂଶ୍ଳେଷଣ (Photosynthesis) ପ୍ରକ୍ରିୟା ଦ୍ୱାରା ନିଜର ଖାଦ୍ୟ ପ୍ରସ୍ତୁତ କରନ୍ତି । ଏହି ପ୍ରକ୍ରିୟାରେ ସେମାନେ ସୂର୍ଯ୍ୟାଲୋକ, ଅଙ୍ଗାରକାମ୍ଳ (CO₂) ଓ ଜଳ (H₂O) ବ୍ୟବହାର କରି ଶର୍କରା (ଖାଦ୍ୟ) ଓ ଅମ୍ଳଜାନ (O₂) ଉତ୍ପାଦନ କରନ୍ତି ।
(ଖ) ଏଥିପାଇଁ ସବୁଜ ଉଦ୍ଭିଦ କେଉଁଠୁ ଶକ୍ତି ପାଏ ?
ସବୁଜ ଉଦ୍ଭିଦମାନେ ଆଲୋକ ସଂଶ୍ଳେଷଣ ପାଇଁ ମୁଖ୍ୟତଃ ସୂର୍ଯ୍ୟାଲୋକରୁ ଶକ୍ତି ପାଆନ୍ତି । ସୂର୍ଯ୍ୟାଲୋକର ଆଲୋକ ଶକ୍ତି ରାସାୟନିକ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ ହୋଇ ଉଦ୍ଭିଦର ଖାଦ୍ୟରେ ଗଚ୍ଛିତ ରହେ ।
(ଗ) ବାୟୁମଣ୍ଡଳରେ ବାୟୁ କିଭଳି ଭାବେ ଗୋଟିଏ ଜାଗାରୁ ଆଉ ଗୋଟିଏ ଜାଗାକୁ ଚଳପ୍ରଚଳ କରେ ?
ସୂର୍ଯ୍ୟଙ୍କ ତାପ ଯୋଗୁଁ ପୃଥିବୀର ବିଭିନ୍ନ ଅଞ୍ଚଳରେ ତାପମାତ୍ରା ଭିନ୍ନ ଭିନ୍ନ ହୁଏ । ଉଷ୍ମ ବାୟୁ ହାଲୁକା ହୋଇ ଉପରକୁ ଉଠେ ଏବଂ ଥଣ୍ଡା ବାୟୁ ଭାରି ହୋଇ ତଳକୁ ଖସେ । ଏହି ତାପମାତ୍ରା ପାର୍ଥକ୍ୟ ଯୋଗୁଁ ବାୟୁମଣ୍ଡଳରେ ଚାପ ପାର୍ଥକ୍ୟ ସୃଷ୍ଟି ହୁଏ, ଯାହା ବାୟୁକୁ ଗୋଟିଏ ଜାଗାରୁ ଆଉ ଗୋଟିଏ ଜାଗାକୁ ଚଳପ୍ରଚଳ କରାଏ ଏବଂ ପବନ ସୃଷ୍ଟି ହୁଏ । ଏଠାରେ ତାପ ଶକ୍ତି ଗତିଜ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ ହୁଏ ।
(ଘ) କୋଇଲା, ପେଟ୍ରୋଲିୟମ ଭଳି ଇନ୍ଧନ ପ୍ରକୃତିରେ କିପରି ପ୍ରସ୍ତୁତ ହୁଏ ?
କୋଇଲା ଓ ପେଟ୍ରୋଲିୟମ ଭଳି ଜୀବାଶ୍ମ ଇନ୍ଧନ ଲକ୍ଷ ଲକ୍ଷ ବର୍ଷ ପୂର୍ବେ ଜୀବିତ ଥିବା ଉଦ୍ଭିଦ ଓ ପ୍ରାଣୀମାନଙ୍କର ଅବଶେଷରୁ ସୃଷ୍ଟି ହୁଏ । ଏହି ଉଦ୍ଭିଦ ଓ ପ୍ରାଣୀମାନେ ସୂର୍ଯ୍ୟାଲୋକରୁ ଶକ୍ତି ଗ୍ରହଣ କରି ତାହାକୁ ରାସାୟନିକ ଶକ୍ତି ରୂପରେ ନିଜ ଶରୀରରେ ଗଚ୍ଛିତ ରଖିଥିଲେ । ମୃତ୍ୟୁ ପରେ ସେମାନଙ୍କର ଅବଶେଷ ଭୂମି ତଳେ ଚାପ ଓ ତାପ ଯୋଗୁଁ ରାସାୟନିକ ଶକ୍ତିରେ ଭରପୂର ଜୀବାଶ୍ମ ଇନ୍ଧନରେ ପରିଣତ ହୁଏ ।
(ଙ) କେଉଁ ପ୍ରକାରର ଶକ୍ତି ରୂପାନ୍ତରଣ ଜଳଚକ୍ରକୁ ସାହାଯ୍ୟ କରିଥାଏ ?
ଜଳଚକ୍ରରେ ସୂର୍ଯ୍ୟଙ୍କ ତାପ ଶକ୍ତି ଜଳକୁ ବାଷ୍ପରେ ପରିଣତ କରି ଉପରକୁ ଉଠାଏ (ତାପ ଶକ୍ତି → ସ୍ଥିତିଜ ଶକ୍ତି) । ଏହି ବାଷ୍ପ ଘନୀଭୂତ ହୋଇ ବର୍ଷା ଆକାରରେ ତଳକୁ ଖସେ (ସ୍ଥିତିଜ ଶକ୍ତି → ଗତିଜ ଶକ୍ତି) । ଏହି ପ୍ରକ୍ରିୟାରେ ତାପ ଶକ୍ତିରୁ ଯାନ୍ତ୍ରିକ ଶକ୍ତିରେ ରୂପାନ୍ତରଣ ଜଳଚକ୍ରକୁ ସାହାଯ୍ୟ କରିଥାଏ ।
ତୁମ ପାଇଁ କାମ : ୮.୭ (ପୃଷ୍ଠା ୯)
ଆମେ ଦୈନନ୍ଦିନ ଜୀବନରେ ବ୍ୟବହାର କରୁଥିବା ବିଭିନ୍ନ ଯନ୍ତ୍ରପାତି କାର୍ଯ୍ୟ କରୁଥିବା ବେଳେ ଓ ଆମମାନଙ୍କର ବିଭିନ୍ନ କାର୍ଯ୍ୟକଳାପରେ ଶକ୍ତି ଗୋଟିଏ ରୂପରୁ ଆଉ ଗୋଟିଏ ରୂପକୁ ରୂପାନ୍ତରିତ ହୋଇଥାଏ । ଏପରି ଶକ୍ତି ରୂପାନ୍ତରଣର ଏକ ତାଲିକା ପ୍ରସ୍ତୁତ କର ଏବଂ ତାହା ସହିତ ସଂଲଗ୍ନ ଯନ୍ତ୍ରପାତିର ନାମ ଲେଖ । ପ୍ରତ୍ୟେକ ଯନ୍ତ୍ରପାତି ଓ କାର୍ଯ୍ୟକଳାପ ସହିତ ସଂପୃକ୍ତ ଶକ୍ତି ରୂପାନ୍ତରଣର ପ୍ରକ୍ରିୟାକୁ ଅନୁଧ୍ୟାନ କର ଏବଂ ତାହାକୁ ଲେଖ ।
ଉତ୍ତର:
ଦୈନନ୍ଦିନ ଜୀବନରେ ଶକ୍ତି ରୂପାନ୍ତରଣର ତାଲିକା:
| ଯନ୍ତ୍ରପାତି / କାର୍ଯ୍ୟକଳାପ | ଶକ୍ତି ରୂପାନ୍ତରଣ |
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୩. ପାଠ୍ୟପୁସ୍ତକ ଅଭ୍ୟାସ ପ୍ରଶ୍ନାବଳୀର ୧୦୦% ସମ୍ପୂର୍ଣ୍ଣ ସମାଧାନ (100% Complete Solved Exercises)
Q1. ନିମ୍ନଲିଖୂତ ଉଦାହରଣଗୁଡ଼ିକୁ ଅନୁଧ୍ୟାନ କର । କାର୍ଯ୍ୟର ସଂଜ୍ଞାନୁସାରେ ଏଥିମଧ୍ୟରୁ ଯେଉଁ କ୍ଷେତ୍ରରେ କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହୋଇଛି, ତାହାର ସୂଚନା ଦିଅ ।
(a) କଳ୍ପନା ଗୋଟିଏ ପୋଖରୀରେ ପହଁରୁଛି ।
(b) ଗୋଟିଏ ଗଧ ନିଜ ପିଠି ଉପରେ ଜିନିଷ ନେଇଯାଉଛି ।
(c) ପବନ ଚକି କୂଅରୁ ପାଣି ଉଠାଉଛି ।
(d) ଗୋଟିଏ ସବୁଜ ଉଦ୍ଭିଦ ଆଲୋକ ସଂଶ୍ଳେଷଣ ପ୍ରକ୍ରିୟାରେ ଖାଦ୍ୟ ପ୍ରସ୍ତୁତ କରୁଛି ।
(e) ଗୋଟିଏ ଇଞ୍ଜିନ୍ ରେଳଗାଡ଼ିକୁ ଟାଣୁଛି ।
(f) ସୂର୍ଯ୍ୟକିରଣରେ ଖାଦ୍ୟଶସ୍ୟଗୁଡ଼ିକୁ ଶୁଖାଯାଉଛି ।
(g) ଗୋଟିଏ ପାଲଟଣା ଜାହାଜ ପବନ ଯୋଗୁଁ ଦରିଆରେ ଭାସି ଭାସି ଚାଲୁଛି ।
ଉତ୍ତର:
କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହେବା ପାଇଁ ବଳ ପ୍ରୟୋଗ ହେବା ଓ ବସ୍ତୁର ବିସ୍ଥାପନ ଘଟିବା ଆବଶ୍ୟକ । ଏହି ନିୟମ ଅନୁଯାୟୀ:
(a) କଳ୍ପନା ଗୋଟିଏ ପୋଖରୀରେ ପହଁରୁଛି ।
(b) ଗୋଟିଏ ଗଧ ନିଜ ପିଠି ଉପରେ ଜିନିଷ ନେଇଯାଉଛି ।
(c) ପବନ ଚକି କୂଅରୁ ପାଣି ଉଠାଉଛି ।
(d) ଗୋଟିଏ ସବୁଜ ଉଦ୍ଭିଦ ଆଲୋକ ସଂଶ୍ଳେଷଣ ପ୍ରକ୍ରିୟାରେ ଖାଦ୍ୟ ପ୍ରସ୍ତୁତ କରୁଛି ।
(e) ଗୋଟିଏ ଇଞ୍ଜିନ୍ ରେଳଗାଡ଼ିକୁ ଟାଣୁଛି ।
(f) ସୂର୍ଯ୍ୟକିରଣରେ ଖାଦ୍ୟଶସ୍ୟଗୁଡ଼ିକୁ ଶୁଖାଯାଉଛି ।
(g) ଗୋଟିଏ ପାଲଟଣା ଜାହାଜ ପବନ ଯୋଗୁଁ ଦରିଆରେ ଭାସି ଭାସି ଚାଲୁଛି ।
Q2. ସର୍କସରେ ରହିଥିବା ଏକ ବିରାଟ ବଡ଼ ଲୁହା ଜାଲିର ଗ୍ଲୋବ୍ (globe) ଭିତରେ ଏକ ମଟର ବାଇକ୍ ଚାଳକ ଦ୍ରୁତ ବେଗରେ ମଟର ବାଇକ୍ ଚଳାଇ, ଗ୍ଲୋବ୍ର ଭିତର ପୃଷ୍ଠରେ ଘୂର୍ଶନ କରି ଗ୍ଲୋବ୍ର ନିମ୍ନତମ ସ୍ଥାନରୁ ଭୂଲମ୍ବ ଦିଗରେ ଶୀର୍ଷତମ ସ୍ଥାନକୁ ଯାଇ ପୁଣି ନିମ୍ନତମ ସ୍ଥାନକୁ ଫେରିଆସିଲେ ମୋଟ୍ କାର୍ଯ୍ୟ କେତେ ସମ୍ପାଦିତ ହୁଏ ?
ଉତ୍ତର:
ଏହି କ୍ଷେତ୍ରରେ, ମଟର ବାଇକ୍ ଚାଳକ ଗ୍ଲୋବ୍ ଭିତରେ ଏକ ବୃତ୍ତାକାର ପଥରେ ଗତି କରୁଛି । ଯେତେବେଳେ ଚାଳକ ନିମ୍ନତମ ସ୍ଥାନରୁ ଶୀର୍ଷତମ ସ୍ଥାନକୁ ଯାଏ, ସେତେବେଳେ ମାଧ୍ୟାକର୍ଷଣ ବଳ ବିରୁଦ୍ଧରେ କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହୁଏ (ବିଯୁକ୍ତାତ୍ମକ କାର୍ଯ୍ୟ) । ଯେତେବେଳେ ସେ ଶୀର୍ଷତମ ସ୍ଥାନରୁ ପୁଣି ନିମ୍ନତମ ସ୍ଥାନକୁ ଫେରିଆସେ, ସେତେବେଳେ ମାଧ୍ୟାକର୍ଷଣ ବଳ ଦ୍ୱାରା କାର୍ଯ୍ୟ ସମ୍ପାଦିତ ହୁଏ (ଯୁକ୍ତାତ୍ମକ କାର୍ଯ୍ୟ) ।
ଯଦି ବାୟୁ ପ୍ରତିରୋଧ ଓ ଘର୍ଷଣ ବଳକୁ ଉପେକ୍ଷା କରାଯାଏ, ତେବେ ନିମ୍ନତମ ସ୍ଥାନରୁ ଶୀର୍ଷତମ ସ୍ଥାନକୁ ଯିବା ପାଇଁ ସମ୍ପାଦିତ କାର୍ଯ୍ୟର ପରିମାଣ ଶୀର୍ଷତମ ସ୍ଥାନରୁ ନିମ୍ନତମ ସ୍ଥାନକୁ ଫେରିବା ପାଇଁ ସମ୍ପାଦିତ କାର୍ଯ୍ୟର ପରିମାଣ ସହିତ ସମାନ କିନ୍ତୁ ବିପରୀତ ଚିହ୍ନଯୁକ୍ତ ହେବ ।
ଉଦାହରଣ ସ୍ୱରୂପ, ଯଦି ନିମ୍ନତମରୁ ଶୀର୍ଷତମକୁ ଯିବା ପାଇଁ କାର୍ଯ୍ୟ W₁ ହୁଏ ଏବଂ ଶୀର୍ଷତମରୁ ନିମ୍ନତମକୁ ଫେରିବା ପାଇଁ କାର୍ଯ୍ୟ W₂ ହୁଏ, ତେବେ W₁ = -W₂ ।
ତେଣୁ, ସମ୍ପୂର୍ଣ୍ଣ ଚକ୍ରରେ ମୋଟ୍ କାର୍ଯ୍ୟ = W₁ + W₂ = W₁ + (-W₁) = 0 ।
ଅତଏବ, ମୋଟ୍ କାର୍ଯ୍ୟ ଶୂନ ହୁଏ ।
Q3. ମୁକ୍ତଭାବେ ଖସୁଥିବା ଏକ ବସ୍ତୁର ସ୍ଥିତିଜ ଶକ୍ତି କ୍ରମାଗତଭାବେ ହ୍ରାସ ପାଉଛି । ଏହା ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମକୁ ଖଣ୍ଡନ କରୁଛି କି ? ତୁମ ଉତ୍ତରର ଯଥାର୍ଥତା ବୁଝାଅ ।
ଉତ୍ତର: ନା, ମୁକ୍ତଭାବେ ଖସୁଥିବା ଏକ ବସ୍ତୁର ସ୍ଥିତିଜ ଶକ୍ତି କ୍ରମାଗତଭାବେ ହ୍ରାସ ପାଇବା ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମକୁ ଖଣ୍ଡନ କରୁନାହିଁ ।
ଯଥାର୍ଥତା: ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମ ଅନୁଯାୟୀ, ଶକ୍ତିର ସୃଷ୍ଟି ନାହିଁ କିମ୍ବା ବିନାଶ ନାହିଁ, ଏହା କେବଳ ଗୋଟିଏ ରୂପରୁ ଅନ୍ୟ ଏକ ରୂପକୁ ରୂପାନ୍ତରିତ ହୋଇଥାଏ । ମୁକ୍ତଭାବେ ଖସୁଥିବା ବସ୍ତୁ କ୍ଷେତ୍ରରେ, ଯେତେବେଳେ ବସ୍ତୁ ତଳକୁ ଖସେ, ତାହାର ଉଚ୍ଚତା କମିବା ଯୋଗୁଁ ସ୍ଥିତିଜ ଶକ୍ତି (E_p = mgh) ହ୍ରାସ ପାଏ । କିନ୍ତୁ ଏହି ସମୟରେ ବସ୍ତୁର ବେଗ ବଢ଼ିବା ଯୋଗୁଁ ତାହାର ଗତିଜ ଶକ୍ତି (E_k = (1/2)mv²) ବୃଦ୍ଧି ପାଏ । ହ୍ରାସ ପାଉଥିବା ସ୍ଥିତିଜ ଶକ୍ତି ଗତିଜ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ ହୁଏ । ଯଦି ବାୟୁ ପ୍ରତିରୋଧକୁ ଉପେକ୍ଷା କରାଯାଏ, ତେବେ ବସ୍ତୁର ମୋଟ ଯାନ୍ତ୍ରିକ ଶକ୍ତି (E_p + E_k) ସର୍ବଦା ସ୍ଥିର ରହେ । ତେଣୁ, ଏହା ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମକୁ ଖଣ୍ଡନ କରୁନାହିଁ ।
Q4. ତମେ ସାଇକେଲ୍ ଚଳାଇବା ବେଳେ ଶକ୍ତି କେଉଁ ରୂପରୁ କେଉଁ ରୂପକୁ ରୂପାନ୍ତରିତ ହୋଇଥାଏ, ତାହା ବର୍ଣ୍ଣନା କର ।
ଉତ୍ତର: ସାଇକେଲ୍ ଚଳାଇବା ବେଳେ ଶକ୍ତିର ନିମ୍ନଲିଖିତ ରୂପାନ୍ତରଣ ଘଟେ:
୧. ରାସାୟନିକ ଶକ୍ତି → ଯାନ୍ତ୍ରିକ ଶକ୍ତି (ଗତିଜ ଶକ୍ତି): ଆମ ଶରୀରରେ ଥିବା ଖାଦ୍ୟର ରାସାୟନିକ ଶକ୍ତି ମାଂସପେଶୀ ଦ୍ୱାରା ଯାନ୍ତ୍ରିକ ଶକ୍ତିରେ (ସାଇକେଲ୍କୁ ଗତି କରାଇବା ପାଇଁ ଗତିଜ ଶକ୍ତି) ରୂପାନ୍ତରିତ ହୁଏ ।
୨. ଯାନ୍ତ୍ରିକ ଶକ୍ତି → ତାପ ଶକ୍ତି: ସାଇକେଲ୍ ଚଳାଇବା ସମୟରେ ଟାୟାର ଓ ରାସ୍ତା ମଧ୍ୟରେ, ବ୍ରେକ୍ ଓ ରିମ୍ ମଧ୍ୟରେ ଘର୍ଷଣ ଯୋଗୁଁ କିଛି ଯାନ୍ତ୍ରିକ ଶକ୍ତି ତାପ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ ହୁଏ । ଆମ ଶରୀରରେ ମଧ୍ୟ କିଛି ରାସାୟନିକ ଶକ୍ତି ତାପ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ ହୋଇ ଶରୀରକୁ ଉଷ୍ମ ରଖେ ।
୩. ଯାନ୍ତ୍ରିକ ଶକ୍ତି → ଶବ୍ଦ ଶକ୍ତି: ସାଇକେଲ୍ ଚଳାଇବା ବେଳେ ଚେନ୍, ଗିଅର ଓ ଅନ୍ୟାନ୍ୟ ଅଂଶର ଘର୍ଷଣ ଯୋଗୁଁ କିଛି ଶବ୍ଦ ଶକ୍ତି ଉତ୍ପନ୍ନ ହୁଏ ।
Q5. ଗୋଟିଏ ଇଲେକ୍ଟ୍ରିକ ହିଟରର ପାୱାର 1500 ୱାଟ୍ । ଏହା 10 ଘଣ୍ଟାରେ କେତେ ଶକ୍ତି ବ୍ୟବହାର କରିବ ?
ଉତ୍ତର:
ଇଲେକ୍ଟ୍ରିକ ହିଟରର ପାୱାର, P = 1500 ୱାଟ୍ = 1.5 କିଲୋୱାଟ୍ (କାରଣ 1 kW = 1000 W)
ବ୍ୟବହାର ସମୟ, t = 10 ଘଣ୍ଟା
ବ୍ୟବହୃତ ଶକ୍ତି, E = P × t
E = 1.5 କିଲୋୱାଟ୍ × 10 ଘଣ୍ଟା
E = 15 କିଲୋୱାଟ ଘଣ୍ଟା (kWh)
ଅତଏବ ଇଲେକ୍ଟ୍ରିକ ହିଟରଟି ୧୦ ଘଣ୍ଟାରେ ୧୫ କିଲୋୱାଟ ଘଣ୍ଟା ଶକ୍ତି ବ୍ୟବହାର କରିବ ।
Q6. (m) ବସ୍ତୁତ୍ଵ ଥିବା ଗୋଟିଏ ବସ୍ତୁ ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ପରିବେଗ (v) ରେ ଗତି କରୁଛି । ଏହି ବସ୍ତୁକୁ ସ୍ଥିର ଅବସ୍ଥାକୁ ଆଣିବାକୁ ହେଲେ କେତେ ପରିମାଣର କାର୍ଯ୍ୟ କରିବାକୁ ହେବ ?
ଉତ୍ତର:
ଗତି କରୁଥିବା ବସ୍ତୁର ଗତିଜ ଶକ୍ତି, E_k = (1/2)mv²
ବସ୍ତୁକୁ ସ୍ଥିର ଅବସ୍ଥାକୁ ଆଣିବାକୁ ହେଲେ, ତାହାର ସମସ୍ତ ଗତିଜ ଶକ୍ତିକୁ ଶୂନ କରିବାକୁ ପଡ଼ିବ । ଏଥିପାଇଁ ବସ୍ତୁ ଉପରେ ତାହାର ଗତିର ବିପରୀତ ଦିଗରେ ବଳ ପ୍ରୟୋଗ କରି କାର୍ଯ୍ୟ କରିବାକୁ ହେବ ।
କାର୍ଯ୍ୟ-ଶକ୍ତି ଉପପାଦ୍ୟ (Work-Energy Theorem) ଅନୁଯାୟୀ, ବସ୍ତୁ ଉପରେ ସମ୍ପାଦିତ ମୋଟ କାର୍ଯ୍ୟ ତାହାର ଗତିଜ ଶକ୍ତିର ପରିବର୍ତ୍ତନ ସହିତ ସମାନ ।
ପ୍ରାରମ୍ଭିକ ଗତିଜ ଶକ୍ତି = (1/2)mv²
ଅନ୍ତିମ ଗତିଜ ଶକ୍ତି (ସ୍ଥିର ଅବସ୍ଥାରେ) = 0
ସମ୍ପାଦିତ କାର୍ଯ୍ୟ, W = ଅନ୍ତିମ ଗତିଜ ଶକ୍ତି - ପ୍ରାରମ୍ଭିକ ଗତିଜ ଶକ୍ତି
W = 0 - (1/2)mv²
W = -(1/2)mv²
ଅତଏବ, ବସ୍ତୁକୁ ସ୍ଥିର ଅବସ୍ଥାକୁ ଆଣିବାକୁ ହେଲେ (1/2)mv² ପରିମାଣର କାର୍ଯ୍ୟ କରିବାକୁ ହେବ । ଏହି କାର୍ଯ୍ୟ ବିଯୁକ୍ତାତ୍ମକ ହେବ କାରଣ ବଳ ବିସ୍ଥାପନର ବିପରୀତ ଦିଗରେ ପ୍ରୟୋଗ ହେବ ।
Q7. 1500 କିଗ୍ରା ବସ୍ତୁତ୍ଵ ବିଶିଷ୍ଟ ଗୋଟିଏ ମୋଟରକାର ଘଣ୍ଟା ପ୍ରତି 60 କି.ମି. ବେଗରେ ଗତି କରୁଛି । ତାହାକୁ ସ୍ଥିର ଅବସ୍ଥାକୁ ଆଣିବାକୁ ହେଲେ କେତେ ପରିମାଣର କାର୍ଯ୍ୟ କରିବାକୁ ହେବ ?
ଉତ୍ତର:
ମୋଟରକାରର ବସ୍ତୁତ୍ଵ, m = 1500 କିଗ୍ରା
ମୋଟରକାରର ବେଗ, v = 60 କିମି/ଘଣ୍ଟା
ବେଗକୁ ମିଟର/ସେକେଣ୍ଡକୁ ପରିବର୍ତ୍ତନ କରିବା:
v = 60 × (୫/୧୮) ମି/ସେ
v = ୧୦୦/୩ ମି/ସେ = ୩୩.୩୩ ମି/ସେ (ପ୍ରାୟ)
କାର୍ର ଗତିଜ ଶକ୍ତି, E_k = (1/2)mv²
E_k = (1/2) × 1500 କିଗ୍ରା × (୧୦୦/୩ ମି/ସେ)²
E_k = 750 × (୧୦୦୦୦/୯) ଜୁଲ୍
E_k = 7500000 / 9 ଜୁଲ୍
E_k = 833333.33 ଜୁଲ୍ (ପ୍ରାୟ)
ବସ୍ତୁକୁ ସ୍ଥିର ଅବସ୍ଥାକୁ ଆଣିବାକୁ ହେଲେ, ତାହାର ସମସ୍ତ ଗତିଜ ଶକ୍ତିକୁ ଶୂନ କରିବାକୁ ପଡ଼ିବ ।
ସମ୍ପାଦିତ କାର୍ଯ୍ୟ, W = ଅନ୍ତିମ ଗତିଜ ଶକ୍ତି - ପ୍ରାରମ୍ଭିକ ଗତିଜ ଶକ୍ତି
W = 0 - E_k
W = -833333.33 ଜୁଲ୍
ଅତଏବ, ମୋଟରକାରକୁ ସ୍ଥିର ଅବସ୍ଥାକୁ ଆଣିବାକୁ ହେଲେ ୮୩୩୩୩୩.୩୩ ଜୁଲ୍ ପରିମାଣର କାର୍ଯ୍ୟ କରିବାକୁ ହେବ । (ଏହି କାର୍ଯ୍ୟ ବିଯୁକ୍ତାତ୍ମକ ହେବ କାରଣ ବଳ ଗତିର ବିପରୀତ ଦିଗରେ ପ୍ରୟୋଗ ହେବ) ।
୧. ଏଠାରେ ଧନୁରେ କେଉଁ ଶକ୍ତି ସଞ୍ଚୁତ ଅଛି ?
ଉତ୍ତର: ଧନୁକୁ ଟାଣିବା ଦ୍ୱାରା ତାହାର ଆକୃତିରେ ପରିବର୍ତ୍ତନ ଘଟେ । ଏହି ବିନ୍ୟାସଗତ ପରିବର୍ତ୍ତନ ଯୋଗୁଁ ଧନୁରେ ସ୍ଥିତିସ୍ଥାପକ ସ୍ଥିତିଜ ଶକ୍ତି (Elastic Potential Energy) ସଞ୍ଚୁତ ହୋଇ ରହିଥାଏ ।
୨. ଏଠାରେ କେଉଁ ଶକ୍ତି କେଉଁ ଶକ୍ତିକୁ ରୂପାନ୍ତରିତ ହେଉଛି ? (ଇଲେକ୍ଟ୍ରିକ ହିଟର ଚିତ୍ର)
ଉତ୍ତର: ଏଠାରେ ବିଦ୍ୟୁତ୍ ଶକ୍ତି ତାପ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ ହେଉଛି । ଇଲେକ୍ଟ୍ରିକ ହିଟର ବିଦ୍ୟୁତ୍ ଶକ୍ତିକୁ ଉତ୍ତାପରେ ପରିଣତ କରି ଘରକୁ ଗରମ କରେ ।
୩.୩ ତୁମ ପାଇଁ କାମ : ୮.୮ (ପୃଷ୍ଠା ୧୦) ର ସମାଧାନ
୨୦ କିଗ୍ରା ଓଜନ ବିଶିଷ୍ଟ ଗୋଟିଏ ବସ୍ତୁକୁ ଭୂମିଠାରୁ ୪ ମିଟର ଉଚ୍ଚତାରୁ ଖସାଇ ଦିଆଗଲା । ଏହି କ୍ଷେତ୍ରରେ ନିମ୍ନଲିଖୂତ ଟେବୁଲରେ ଦର୍ଶାଯାଇଥୁବା ଭଳି ପ୍ରତ୍ୟେକ ସ୍ଥାନରେ ବସ୍ତୁଟିର ସ୍ଥିତିଜ ଶକ୍ତି ଓ ଗତିଜ ଶକ୍ତିକୁ ହିସାବ କରି ଶୂନ୍ୟସ୍ଥାନ ପୂରଣ କର । (ହିସାବକୁ ସରଳ କରିବା ପାଇଁ g = 10 ମି/ସେ² ନିଅ)
ଉତ୍ତର:
ବସ୍ତୁର ବସ୍ତୁତ୍ଵ, m = ୨୦ କିଗ୍ରା
ମାଧ୍ୟାକର୍ଷଣଜନିତ ତ୍ୱରଣ, g = ୧୦ ମି/ସେ²
ମୋଟ ଉଚ୍ଚତା, H = ୪ ମିଟର
ମୋଟ ଯାନ୍ତ୍ରିକ ଶକ୍ତି (E_Total) = E_p + E_k = ସ୍ଥିର ।
ପ୍ରାରମ୍ଭରେ (h = ୪ ମିଟର), ବସ୍ତୁ ସ୍ଥିର ଥିବାରୁ E_k = 0 ।
E_Total = mgh + 0 = ୨୦ କିଗ୍ରା × ୧୦ ମି/ସେ² × ୪ ମି = ୮୦୦ ଜୁଲ୍ ।
ତେଣୁ, ମୋଟ ଯାନ୍ତ୍ରିକ ଶକ୍ତି ସର୍ବଦା ୮୦୦ ଜୁଲ୍ ରହିବ ।
| ବସ୍ତୁଟିର ଅବସ୍ଥାନ ଉଚ୍ଚତା (ମି) (h) | ବସ୍ତୁର ସ୍ଥିତିଜ ଶକ୍ତି E_p = mgh (ଜୁଲ୍) | ବସ୍ତୁର ଗତିଜ ଶକ୍ତି E_k = (1/2)mv² (ଜୁଲ୍) | ବସ୍ତୁର ମୋଟ ଯାନ୍ତ୍ରିକ ଶକ୍ତି E_p + E_k (ଜୁଲ୍) |
|---|---|---|---|
| ୪ | ୨୦ × ୧୦ × ୪ = ୮୦୦ | ୦ | ୮୦୦ + ୦ = ୮୦୦ |
| ୩ | ୨୦ × ୧୦ × ୩ = ୬୦୦ | ୮୦୦ - ୬୦୦ = ୨୦୦ | ୬୦୦ + ୨୦୦ = ୮୦୦ |
| ୨ | ୨୦ × ୧୦ × ୨ = ୪୦୦ | ୮୦୦ - ୪୦୦ = ୪୦୦ | ୪୦୦ + ୪୦୦ = ୮୦୦ |
| ୧ | ୨୦ × ୧୦ × ୧ = ୨୦୦ | ୮୦୦ - ୨୦୦ = ୬୦୦ | ୨୦୦ + ୬୦୦ = ୮୦୦ |
| ଭୂମିର ଠିକ୍ ଉପରେ (୦) | ୨୦ × ୧୦ × ୦ = ୦ | ୮୦୦ - ୦ = ୮୦୦ | ୦ + ୮୦୦ = ୮୦୦ |
୩.୪ ତୁମ ପାଇଁ କାମ : ୮.୯ (ପୃଷ୍ଠା ୧୧) ର ସମାଧାନ
ମନେକର ଦୁଇଜଣ ବାଳକ A ଏବଂ B ଙ୍କର ଓଜନ ସମାନ । ଦୁଇଜଣଜାକ ଏକ ଦୌଡ଼ିକୁ ଧରି ପୃଥକ ପୃଥକଭାବରେ ଉପରକୁ ଆଠ ମିଟର ଉଚ୍ଚତା ପର୍ଯ୍ୟନ୍ତ ଚଢ଼ିଲେ । ଚଢ଼ିବାପାଇଁ A କୁ 15 ସେକେଣ୍ଡ ଓ B କୁ 20 ସେକେଣ୍ଡ ସମୟ ଲାଗିଲା । ଏଠାରେ ଉଭୟ A ଓ B ପ୍ରତ୍ୟେକ କେତେ ପରିମାଣ କାର୍ଯ୍ୟ ସମ୍ପାଦନ କଲେ ? (W=mgh) ।
ଉତ୍ତର:
ବାଳକ A ଓ B ଙ୍କର ଓଜନ ସମାନ । ମନେକର ପ୍ରତ୍ୟେକଙ୍କ ଓଜନ = F ।
ଉଚ୍ଚତା, h = ୮ ମିଟର ।
ସମ୍ପାଦିତ କାର୍ଯ୍ୟ, W = F × h
ଯେହେତୁ ଉଭୟ ବାଳକଙ୍କର ଓଜନ (F) ଓ ଚଢ଼ିଥିବା ଉଚ୍ଚତା (h) ସମାନ, ତେଣୁ ଉଭୟଙ୍କ ଦ୍ୱାରା ସମ୍ପାଦିତ କାର୍ଯ୍ୟର ପରିମାଣ ସମାନ ହେବ ।
W_A = W_B = F × ୮ ଜୁଲ୍ ।
(ପାଠ୍ୟପୁସ୍ତକରେ mg = 400N ଦିଆଯାଇଛି, ତେଣୁ W = 400N × 8m = 3200 ଜୁଲ୍)
ଯଦିଓ ଉଭୟ ସମାନ ପରିମାଣର କାର୍ଯ୍ୟ କଲେ, ମାତ୍ର କାମ କରିବାପାଇଁ B ଅପେକ୍ଷା A କମ୍ ସମୟ ନେଇଛି । ମନରେ ପ୍ରଶ୍ନ ଉଠୁଛି ଯେ, ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ସମୟରେ ବା ପ୍ରତି ଏକ ସେକେଣ୍ଡରେ କିଏ ବେଶି କାମ କରିପାରିଛି ?
ଉତ୍ତର:
ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ସମୟରେ ବା ପ୍ରତି ଏକ ସେକେଣ୍ଡରେ କିଏ ବେଶି କାମ କରିପାରିଛି ତାହା କ୍ଷମତା (Power) ଦ୍ୱାରା ନିର୍ଣ୍ଣୟ କରାଯାଏ ।
ବାଳକ A ର କ୍ଷମତା, P_A = W_A / t_A
P_A = (F × ୮) / ୧୫
ବାଳକ B ର କ୍ଷମତା, P_B = W_B / t_B
P_B = (F × ୮) / ୨୦
ଯେହେତୁ ୧୫ < ୨୦, ତେଣୁ P_A > P_B ।
ଅତଏବ, ବାଳକ A ବାଳକ B ଅପେକ୍ଷା ପ୍ରତି ଏକ ସେକେଣ୍ଡରେ ଅଧିକ କାର୍ଯ୍ୟ କରିପାରିଛି ।
୪. ବୋର୍ଡ ପରୀକ୍ଷା ମାଷ୍ଟ୍ରି ଟିପ୍ସ ଓ ସାଧାରଣ ଭୁଲ୍ (Board Exam Tips & Pitfalls)
ବୋର୍ଡ ପରୀକ୍ଷାରେ ଉତ୍ତମ ନମ୍ବର ରଖିବା ପାଇଁ ନିମ୍ନଲିଖିତ ଟିପ୍ସ ଓ ସାଧାରଣ ଭୁଲ୍ ପ୍ରତି ଧ୍ୟାନ ଦେବା ଆବଶ୍ୟକ:
୪.୧ ପରୀକ୍ଷା ପ୍ରସ୍ତୁତି ରଣନୀତି ଓ ୧୦୦/୧୦୦ ସ୍କୋରିଂ ସିକ୍ରେଟ୍ସ:
୧. ମୌଳିକ ଧାରଣା ସ୍ପଷ୍ଟ କରନ୍ତୁ: କାର୍ଯ୍ୟ, ଶକ୍ତି ଓ କ୍ଷମତାର ସଂଜ୍ଞା, ଏକକ ଓ ସୂତ୍ରଗୁଡ଼ିକୁ ଭଲ ଭାବରେ ବୁଝନ୍ତୁ ।
୨. ସୂତ୍ରଗୁଡ଼ିକୁ ମନେ ରଖନ୍ତୁ: ସମସ୍ତ ଗାଣିତିକ ସୂତ୍ର (W = F × s, E_k = (1/2)mv², E_p = mgh, P = W / t) ଓ ସେମାନଙ୍କର ଏକକଗୁଡ଼ିକୁ ମନେ ରଖନ୍ତୁ ।
୩. ଗାଣିତିକ ପ୍ରଶ୍ନ ଅଭ୍ୟାସ କରନ୍ତୁ: ପାଠ୍ୟପୁସ୍ତକରେ ଥିବା ସମସ୍ତ ଉଦାହରଣ ଓ ଅନୁଶୀଳନୀ ପ୍ରଶ୍ନଗୁଡ଼ିକୁ ବାରମ୍ବାର ଅଭ୍ୟାସ କରନ୍ତୁ । ବିଶେଷ କରି ଏକକ ପରିବର୍ତ୍ତନ (ଯଥା: କିମି/ଘଣ୍ଟା ରୁ ମି/ସେ) ଉପରେ ଧ୍ୟାନ ଦିଅନ୍ତୁ ।
୪. ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମ: ଏହି ନିୟମକୁ ଭଲ ଭାବରେ ବୁଝନ୍ତୁ ଓ ମୁକ୍ତ ପତନ କ୍ଷେତ୍ରରେ ଏହାର ପ୍ରୟୋଗକୁ ମନେ ରଖନ୍ତୁ ।
୫. ଚିତ୍ର ଓ ଉଦାହରଣ: ପ୍ରତ୍ୟେକ ଧାରଣା ପାଇଁ ବାସ୍ତବ ଜୀବନର ଉଦାହରଣ ଓ ଆବଶ୍ୟକ ସ୍ଥଳେ ଚିତ୍ର ଅଙ୍କନ କରି ବୁଝାଇବାକୁ ଚେଷ୍ଟା କରନ୍ତୁ ।
୬. ପୂର୍ବ ବର୍ଷର ପ୍ରଶ୍ନପତ୍ର ଅଭ୍ୟାସ: ପୂର୍ବ ବର୍ଷର ପ୍ରଶ୍ନପତ୍ରଗୁଡ଼ିକୁ ସମୟ ସୀମା ମଧ୍ୟରେ ସମାଧାନ କରିବା ଦ୍ୱାରା ଆତ୍ମବିଶ୍ୱାସ ବଢ଼ିବ ।
୪.୨ ସାଧାରଣ ଭୁଲ୍ (Common Pitfalls):
୧. କାର୍ଯ୍ୟର ସଂଜ୍ଞାକୁ ଭୁଲ୍ ବୁଝିବା: ଦୈନନ୍ଦିନ ଜୀବନର କାର୍ଯ୍ୟ ଓ ବୈଜ୍ଞାନିକ କାର୍ଯ୍ୟ ମଧ୍ୟରେ ଥିବା ପାର୍ଥକ୍ୟକୁ ବୁଝି ନପାରିବା । (ଯଥା: ମୁଣ୍ଡରେ ବୋଝ ମୁଣ୍ଡେଇ ଚାଲିବା କ୍ଷେତ୍ରରେ କାର୍ଯ୍ୟ ଶୂନ) ।
୨. ଏକକରେ ଭୁଲ୍: ଗାଣିତିକ ପ୍ରଶ୍ନରେ ଏକକଗୁଡ଼ିକୁ ଠିକ୍ ଭାବରେ ପରିବର୍ତ୍ତନ ନକରିବା (ଯଥା: କିମି/ଘଣ୍ଟା କୁ ମି/ସେ ରେ ପରିବର୍ତ୍ତନ ନକରିବା) ।
୩. କାର୍ଯ୍ୟର ଚିହ୍ନ (Sign of Work): ବଳ ଓ ବିସ୍ଥାପନର ଦିଗ ଅନୁଯାୟୀ କାର୍ଯ୍ୟ ଯୁକ୍ତାତ୍ମକ ବା ବିଯୁକ୍ତାତ୍ମକ ହେବ, ଏହାକୁ ଭୁଲ୍ କରିବା ।
୪. ଗତିଜ ଓ ସ୍ଥିତିଜ ଶକ୍ତିର ସୂତ୍ରରେ ଭୁଲ୍: E_k = (1/2)mv² ଓ E_p = mgh ସୂତ୍ରଗୁଡ଼ିକୁ ଠିକ୍ ଭାବରେ ପ୍ରୟୋଗ ନକରିବା ।
୫. ଶକ୍ତି ସଂରକ୍ଷଣ ନିୟମର ଅବଧାରଣା: ମୁକ୍ତ ପତନ କ୍ଷେତ୍ରରେ ମୋଟ ଯାନ୍ତ୍ରିକ ଶକ୍ତି ସ୍ଥିର ରହେ, ଏହି ଧାରଣାକୁ ଭୁଲ୍ କରିବା ।
୬. କ୍ଷମତା ଓ ଶକ୍ତି ମଧ୍ୟରେ ପାର୍ଥକ୍ୟ: କ୍ଷମତା ହେଉଛି କାର୍ଯ୍ୟ କରିବାର ହାର, କିନ୍ତୁ ଶକ୍ତି ହେଉଛି କାର୍ଯ୍ୟ କରିବାର ସାମର୍ଥ୍ୟ । ଏହି ପାର୍ଥକ୍ୟକୁ ଭୁଲ୍ କରିବା ।
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(ନୋଟ୍ସ ପ୍ରସ୍ତୁତି: ଉତ୍କଳ ସ୍କିଲ୍ ସେଣ୍ଟର - BSE Odisha 100% Full Textbook Master Edition)
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