Two carts, one twice as heavy as the other, are at rest on a horizontal track. A person pushes each cart for 8 s. Ignoring friction and assuming equal force exerted on both carts, the kinetic energy of the heavy cart after the push compared to the kinetic energy of the light cart is:.
A) 1/4 K.
B) 1/2 K.
C) K.
D) 2K.
E) 4K.

The correct option is: B that is 1/2 K

Explanation:

Given:

Two carts of different masses, same force were applied for same duration of time.

Mass of the lighter cart =

Mass of the heavier cart =

We have to find the relationship between their kinetic energy:

Let the KE of cart having mass m be "K".

and KE of cart having mass m be "K1".

As it is given regarding Force and time so we have to bring in picture the concept of momentum Δp and find a relation with KE.

Numerical analysis.

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Now,

Kinetic energies and their ratios in terms of momentum or impulse.

KE (K) of mass m.

⇒           ...equation (i)

KE (K1) of mass 2m.

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⇒         ...equation (ii)

Lets divide K1 and K to find the relationship between the two carts's KE.

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The kinetic energy of the heavy cart after the push compared to the kinetic energy of the light cart is 1/2 K.