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ICSE Class 10 Physics Question 7 of 23

Work, Energy and Power — Question 14

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Question 14

Assertion (A): If momentum of a body increases by 50%, its kinetic energy will increase by 125%.

Reason (R): Kinetic energy is proportional to the square of velocity.

  1. Both A and R are true and R is the correct explanation of A
  2. Both A and R are false and R is not the correct explanation of A
  3. assertion is false but reason is true
  4. assertion is true but reason is false
Answer

Both A and R are true and R is the correct explanation of A.

Explanation

Assertion (A) is true. When the momentum of a body increases by 50%, its kinetic energy will increase by 125%.

Let initial momentum be p and kinetic energy be K

If p increases by 50%, the new momentum p' = p + p2\dfrac{p}{2} = 3p2\dfrac{3p}{2}

Relation between kinetic energy and momentum is given by; K = p22m\dfrac{p^2}{2m}

So, K′K\dfrac{K'}{K} = p′22mp22m\dfrac{\dfrac{p'^2}{2m}}{\dfrac{p^2}{2m}} = p′2p2\dfrac{p'^2}{p^2} = (3p2)2p21\dfrac{\Big(\dfrac{3p}{2}\Big)^2}{\dfrac{p^2}{1}} = 94\dfrac{9}{4}

So,

Percentage increase in kinetic energy = K′−KK\dfrac{K'-K}{K} x 100

= 9K4−KK\dfrac{ \dfrac{9K}{4} -K}{K} x 100

= 9K−4K4K\dfrac{ \dfrac{9K-4K}{4}}{K} x 100

= 5K4K\dfrac{ \dfrac{5K}{4}}{K} x 100

= 54\dfrac{5}{4} x 100 = 125%

Hence, kinetic energy will increase by 125%.

Reason (R) is true. Kinetic energy is proportional to the square of velocity, according to the formula: KE = 12\dfrac{1}{2}mv2.