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Question

Two cars A and B with a mass of 5 kg and 10 kg and initial velocities of 10 ms1 and 5 ms1 are racing. Which car exerts more power before coming to rest? (Time taken for both cars to complete the race is 10 seconds):


A

Data insufficient

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B

B

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C

Both exert same power

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D

A

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Solution

The correct option is D

A


Let W1 be the work done and P1 be the power exerted by car A.
Let W2 be the work done and P2 be the power exerted by car B.
Given mass of car A, m1 = 5 kg
initial velocity of car Au1=10 ms1
final velocity of car A, v1=0 (since the car comes to rest)
mass of car B, m2 = 10 kg
initial velocity of car B u2=5 ms1
final velocity of car B, v2=0 (since the car comes to rest)
Since work done = change in kinetic energy
work done by car A = final K.E - initial K.E = mv212mu212=0mu212
W1 = 12×m1×u12=0.5×5×100=250,
So P1=25010=25 Js1
work done by car B = final K.E - initial K.E = mv212mu212=0mu222
W2​ =12×m2×u22=0.5× 10 × 25 = 125, So P2​ = 12510=12.5 Js1
Hence A exerts more power than B.


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