Question

Three bodies each of masses $1\text{kg},2\text{kg}$ and $3\text{kg}$ slide down a smooth inclined plane starting from rest. Then choose which of the following statements is correct:

• A. $1\text{kg}$ body will have least velocity on reaching bottom of the inclined plane.
• B. $3\text{kg}$ body will have least velocity on reaching bottom of the inclined plane.
• C. $1\text{kg}$ body will take least time on reaching bottom of the inclined plane.
• D. All bodies will have the same velocity and take the same time on reaching bottom of the inclined plane.

Answer 1

The correct option is D All bodies will have the same velocity and take the same time on reaching bottom of the inclined plane.

$a=g\sin \theta$, for a body sliding down a smooth inclined plane. Hence $a$ is independent of the masses of the bodies. Since the displacements are also equal, their final velocity and time of travel are also equal.