$Assertion$ : The position of centre of mass of a body depends upon shape and size of the body.
$Reason$ : Centre of mass of a body lies always at the centre of the body.
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
If the Assertion is correct but Reason is incorrect.
If both the Assertion and Reason are incorrect.
A thin bar of length $L$ has a mass per unit length $\lambda $, that increases linearly with distance from one end. If its total mass is $M$ and its mass per unit length at the lighter end is $\lambda_0$, then the distance of the centre of mass from the lighter end is
As shown in figure, when a spherical cavity (centred at $\mathrm{O})$ of radius $1$ is cut out of a uniform sphere of radius $\mathrm{R} \text { (centred at } \mathrm{C}),$ the centre of mass of remaining (shaded) part of sphere is at $G$, i.e, on the surface of the cavity. $\mathrm{R}$ can be detemined by the equation
Four bodies of masses $2, 3, 5$ and $8\,kg$ are placed at the four corners of a square of side $2\,m$ as shown. The position of $CM$ will be
Three identical spheres, each of mass $1\ kg$ are placed touching each other with their centres on a straight line. Their centres are marked $K, L$ and $M$ respectively. The distance of centre of mass of the system from $K$ is