Question

If the momentum of an object increases by 20%, its kinetic energy will increase by ______.
1. 66%
2. 77%
3. 44%
4. 55%

Answer 1

Correct Answer - Option 3 : 44%

The correct answer is 44%.

• Momentum can be defined as the product of the mass of a particle and its velocity.
• It is denoted by p, SI unit is (Kg-m)/s and Dimension is  MLT⁻¹.
• Newton's second law defines a force to be equal to the change in momentum with a change in time. 

 

If Initial Momentum = p_i, Mass of object = m, and velocity of object = v 

Kinetic Energy, K.E_i = 1/2 (mv²) 

1/2 (mv2) = (1/2 (mv)²)/m = (1/2p²)/m

Now, p increases by 20% , so new momentum,

p_f =( p + 20% of p) = p + p/5 = 6p/5.

New Kinetic Energy =  (1/2p_f2)/m.

So, K.E_f = (1/2 * (6p/5)²)/m = 36/25 * (1/2p2)/m.

% increase in K.E = (Change in K.E/ Initial K.E) * 100

                             =( ( 36/25 * (1/2p2)/m -  (1/2p2)/m) /  (1/2p2)/m) * 100.

So, % increase in K.E = (11/25) * 100 = 44%.

K.E =  1/2 (mv2) =  1/2 (mv)*v.

K.E = 1/2(pv), ---------- 1

But the above equation is wrong to implement in this question.

• Since p = m*v, where mass is always constant, and velocity varies, which means momentum varies because of the velocity.
• In eqn. 1, v is left out, and hence the result thus produced will be wrong.