Work, Energy and Power
- The heart of man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 ×103 kg/m3 and g = 10m/s2 then the power of heart in watt is :
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Power F→ . V→ = P A V→ = ρ gh AV
∵ P = F and P = ρ gh 
A
= 13.6 × 103 × 10 × 150 × 10–3 × 0.5 × 10–3 / 60= 102 = 1.70 watt 60
Correct Option: D
Power F→ . V→ = P A V→ = ρ gh AV
∵ P = F and P = ρ gh A
= 13.6 × 103 × 10 × 150 × 10–3 × 0.5 × 10–3 / 60= 102 = 1.70 watt 60
- A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest the force on the particle at time t is
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As we know power P = dw dt ⇒ w = Pt = 1 mV2 2 
Hence, acceleration
Therefore, force on the particle at time ‘t’
Correct Option: D
As we know power P = dw dt ⇒ w = Pt = 1 mV2 2
Hence, acceleration
Therefore, force on the particle at time ‘t’
- A body of mass 1 kg begins to move under the action of a time dependent force F→ = (2tî + 3t2ĵ) N, where î and ĵ are unit vectors alogn x and y axis. What power will be developed by the force at the time t?
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Given force F→ = 2tî + 3t2ĵ
According to Newton's second law of motion,m dv→ = 2tî + 3t2ĵ (m = 1 kg) dt 
⇒ v→ = t2î + t3ĵ
Power P = F→ . v→ = (2tî + 3t2ĵ) . (t2î + t3ĵ)
= (2t3 + 3t5)WCorrect Option: D
Given force F→ = 2tî + 3t2ĵ
According to Newton's second law of motion,m dv→ = 2tî + 3t2ĵ (m = 1 kg) dt
⇒ v→ = t2î + t3ĵ
Power P = F→ . v→ = (2tî + 3t2ĵ) . (t2î + t3ĵ)
= (2t3 + 3t5)W
- Two bodies of masses m and 4m are moving with equal kinetic energies. The ratio of their linear momenta will be
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K1 = p12 × m2 K2 m1 p22 [ ∵ p = mv ⇒ K = p2 ] 2m 
Correct Option: C
K1 = p12 × m2 K2 m1 p22 [ ∵ p = mv ⇒ K = p2 ] 2m
