A rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time, when the rod makes an angle $\theta$ with horizontal the velocity of $COM$ of the rod is $v_0$ . The velocity of the end of the rod in contact with the surface at that instant is
${v_0}\cot \theta $
${v_0}\cos \theta $
${v_0}\sin \theta $
${v_0}\tan \theta $
Figure shows a thin metallic triangular sheet $ABC.$ The mass of the sheet is $M.$ The moment of inertia of the sheet about side $AC$ is
In the figure shown a ring $A$ is initially rolling without sliding with a velocity $v$ on the horizontal surface of the body $B$ (of same mass as $A$). All surfaces are smooth. $B$ has no initial velocity. What will be the maximum height reached by $A$ on $B$.
A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u,$ the centre of mass of the system (trolley + child) will move with a speed.
Two particles of equal masses have velocities$\overrightarrow {{v_1}} = 2\hat i\,m/s$ and $\overrightarrow {{v_2}} = 2\hat j\,m/s$. The first particle has an acceleration $\overrightarrow {{a_1}} = \left( {3i + 3\hat j} \right)\,m/{s^2}$,while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a
If the earth were to suddenly contract to $1/n^{th}$ of its present radius without any change in its mass, the duration (in $hrs.$ ) of the new day will be nearly