A small disc of radius $2\, cm$ is cut from a disc of radius $6\, cm$. If the distance between their centres is $3.2\, cm$, what is the shift in the centre of mass of the disc ....... $cm$.

From a circular disc of radius $R$, a square is cut out with a radius as its diagonal. The center of mass of remainder part is at a distance (from the centre)

Consider the following statements

Assertion $(A)$ : $A$ cyclist always bends inwards while negotiating a curve

Reason $(R)$ : By bending he lowers his centre of gravity Of these statements,

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

From a circle of radius $a,$ an isosceles right angled triangle with the hypotenuse as the diameter of the circle is removed. The distance of the centre of gravity of the remaining position from the centre of the circle is

The position of the centre of mass of a uniform semi-circular wire of radius $'R'$ placed in $x-y$ plane with its centre at the origin and the line joining its ends as $x$-axis is given by $\left(0, \frac{x R}{\pi}\right)$.

Then, the value of $|x|$ is ...... .