Question

The kinetic energy acquired by the body of mass $\text{'}m\text{'}$after traveling a fixed distance from rest under the action of a constant force is

• A. directly proportional to mass $m$
• B. inversely proportional to mass $m$
• C. inversely proportional to mass $m^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
• D. independent of mass $m$

Answer 1

The correct option is D

independent of mass $m$

According to the question, we have given that

The kinetic energy acquired by the body of mass $\text{'}m\text{'}$after traveling a fixed distance from rest under the action of a constant force

$\Rightarrow K.E=\frac{1}{2}m{v}^2.......\left(i\right)$

To calculate the velocity of kinetic energy. Use the equation of motion of velocity.

$$\begin{gathered} \Rightarrow v^2=u^2+2as \\ \Rightarrow v^2=0+2as \\ \Rightarrow v^2=2as.........\left(ii\right) \\ Fromequation\left(i\right)and\left(ii\right) \\ \Rightarrow K.E=\frac{1}{2}m\times 2as \\ \Rightarrow K.E=\frac{1}{2}m\times 2\frac{F}{m}s \\ \Rightarrow K.E=F.s\left(cons\tan t\right) \end{gathered}$$

Thus, the kinetic energy in the given case is independent of the mass of the body.

Hence, option D is the correct answer.