Question

The kinetic energy acquired by a body of mass $m$ in travelling a certain distance starting from rest, under a constant force is:
A. directly proportional to $m$.
B. directly proportional to $\sqrt m$.
C. inversely proportional to $\sqrt m$.
D. independent of $m$.

Answer 1

Energy is the ability to do work. When a body covers some displacement under the action of a force acting on it is known as energy. Kinetic energy is the energy which is associated with a body in motion. We will derive an equation to understand the relation between kinetic energy and force in terms of mass and displacement to find the required answer.

Complete step by step answer:
In the given question it is stated that when a body of mass $m$ travels a certain distance from rest, under a constant force it acquires kinetic energy.Kinetic energy of a particle is defined as the energy acquired by the particle when it is in motion.Let the constant force that acts on the body is $F$.The mass of the body is given as $m$.Let the body displaces to a small distance $s$.

We know that the work done on the body is the energy transferred.Let the work done be $W$. Thus, Work done$=$Kinetic energy
$\Rightarrow W = F.s =$Kinetic energy
As the force is constant so the kinetic energy is directly proportional to displacement.Hence it is independent of the mass $m$.

Therefore, the correct option is D.

Note: It must be noted that when a body is in motion under the influence of any external force, then it possesses kinetic energy and also it does work. Work is done by a particle when it covers a certain displacement under the influence of a force.