If two bodies of different masses, initially at rest, are acted upon by the same force for the same time, then the both bodies acquire the same: A. Velocity B. Momentum C. Acceleration D. Kinetic energy

Velocity
Momentum
Acceleration
Kinetic energy

The correct answer is: C. Acceleration

The acceleration of an object is the rate at which its velocity changes. The greater the mass of an object, the more force is required to accelerate it. However, if two objects have different masses but are acted upon by the same force for the same time, they will both acquire the same acceleration. This is because the acceleration of an object is independent of its mass.

To understand this, let’s consider the following example. Suppose we have two objects, A and B, with masses $m_A$ and $m_B$, respectively. If these objects are acted upon by the same force $F$ for the same time $t$, then the change in their velocities will be the same. This can be expressed mathematically as follows:

$$\Delta v_A = \Delta v_B$$

The change in velocity is equal to the acceleration times the time interval, so we can rewrite the above equation as follows:

$$a_A t = a_B t$$

Since the time interval is the same for both objects, we can cancel it out to get the following equation:

$$a_A = a_B$$

Therefore, the acceleration of the two objects is the same.

It is important to note that this only applies if the two objects are acted upon by the same force for the same time. If the force or the time interval are different, then the acceleration of the two objects will also be different.