Question

A car is accelerated on a levelled road and attains a velocity $4times$ of its initial velocity. In this process the potential energy of the car
(A) Does not changes
(B) Become twice of initial
(C) Become 4 times of initial
(D) Become 16 times of initial

Answer 1

The potential energy of a body is defined as the energy of a body due to its position and mathematically potential energy is defined as the product of mass of the body, the height up to which it is raised from ground level and the acceleration due to gravity and written as $P.E = mgh$.

Complete answer:
According to the question, we have given that car is moving on a levelled road which means there is no change in height of the level of road from ground level and from definition of potential energy $P.E = mgh$ we know, that potential energy of the body only depends upon the mass of the body and height to which it get raised because $g = 9.8m{s^{ - 2}}$ remains constant (acceleration due to gravity) hence,
when car attains velocity four times of its initial velocity the mass still remains same and the height of the level road also don’t changes so, Potential energy will not change due to change in its velocity of the car according to its formula $P.E = mgh$ ,
$m$ Mass remains same
$h$ Height of levelled road remain same
$g$ Acceleration due to gravity remains constant.
Therefore, potential energy will also remain the same. Hence, the correct option is (A) is correct.

Note:
It should be remembered that, while doing classical mechanics the mass of the body don not changes with velocity but in case of relativistic mechanics, the mass of the body changes with velocity which is called relativistic mass and its calculated as $m = \dfrac{{{m_0}}}{{\sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} }}$ where, ${m_0}$ is rest mass of the body, $c$ is the speed of light.