A body of mass $M$ is moving on a smooth surface with speed $v_0$. Another body of same mass $M$ attached to a spring is kept on the same surface as shown. The moving mass makes an impact with the spring of spring constant $k$ and starts compressing it. What is the maximum compression in the spring?

 

A uniform rod of mass $M$ and length $L$ is standing vertically along the $y-$axis on a smooth horizontal surface as shown. A small disturbance causes the lower end to slip on the smooth horizontal surface and rod starts falling. The path followed by centre of mass of the rod during the fall is

A rigid rod is rotating as well as translating on a smooth horizontal surface. The velocities of its ends at any moment are as shown in figure. If $\theta =60°$, find the value of $v_2$.

A cubical block of height $a$ and $b$ is placed on the horizontal surface with sufficient friction. For a given force.

The moment of inertia of a semi circular disc of mass $M$ and radius $R$ about an axis passing through the point $O$ and perpendicular to the plane of disc is (shown in figure)

Four rods of equal mass $m$ and length $L$ forms a square $ABCD$ as shown in figure. The moment of inertia of $ABCD$ about the axis $O{O}^{\text{'}}$ passing, through the point $A$ lying in the plane of square is

From a uniform sphere of mass $M$ and radius $R$ a cavity of diameter $R$ is created as shown. Find the ratio of moment of inertia of the sphere left about $A{A}^{\text{'}}$ and $B{B}^{\text{'}}$.

A force $\overrightarrow{F}=\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)\mathrm{N}$ is acting on a point mass $m=\left(\frac{1}{2}\right)\mathrm{kg}$ at a point $A\left(2\mathrm{m},2\mathrm{m}\right)$. Find the angular acceleration of the line $OA$ at this instant.