If momentum of an object is increased by 10% then its kinetic energy will increase by

The correct option is B 21 % Step 1: Given Data Let the initial momentum be p. Given, the final momentum p ' = p 1 + 10 % = 11 p 10 Let the initial kinetic energy be K E. Let the mass be m. Let the velocity be v. Step 2: Formula Used K E = 1 2 m v 2 p = m v Step 3: Calculate the Kinetic Energy We know that kinetic energy, K E = 1 2 m v 2 ⇒ K E = 1 2 m . m 2 v 2 ⇒ K E = 1 2 m p 2 ∵ p = m v Now, the final kinetic energy, K E ' = 1 2 m p ' 2 = 1 2 m 121 p 2 100 Step 4: Calculate the Percentage Increase Therefore, change in kinetic energy, △ K E = 1 2 m 121 p 2 100 - 1 2 m p 2 = 1 2 m p 2 121 100 - 1 = 1 2 m p 2 21 100 = K E 21 100 Therefore, the percentage increase in kinetic energy, = 21 100 × 100 = 21 % Hence, the correct answer is option (B).

Hint: To solve this question we will use the relation between kinetic energy and the momentum of a body. The relation between K.E and P is: $K.E = \dfrac \times 100\% \\ \Rightarrow 21\% \\ \] Hence, we can see that if momentum of an object increases by 10%, then the kinetic energy will increase by 21%. Therefore, the correct answer is option (B). Note: Whenever we ask such questions, we first have to remember the relation between the given terms. Then we will find out the value of final momentum and then we will use that value to find the value of final kinetic energy. After that we will use the final value and initial value to find out the increase in kinetic energy. Then we can easily find out the increase %.