Rotational Motion - Mechanics - Physics Previous Year Questions

A particle of mass \(m\) is allowed to fall freely under gravity from a point \(P\) as shown in the figure. If the vector position \(Q\) of the particle from the origin is represented by \(\mathbf{r}\), the magnitude of torque acting on the particle at time \(t\) with respect to the origin \(O\) is.

Consider a rod of mass \(M\) and length \(L\) pivoted at its centre free to rotate in a vertical plane. The rod is at rest in the vertical position. A bullet of mass \(M\) moving horizontal at a speed \(v\) strikes and gets embedded in one end of the rod. The angular velocity of the rod just after the collision will be

A solid sphere having mass \(m\) and radius \(R\) moves down a plane inclined at an angle '\(\theta\)'. Find the ratio between its acceleration when it rolls without slipping and its acceleration when it slides down the same plane without any rotation.

A particle of mass $m$ is projected with a velocity \(v\) making an angle of \(45^{\circ}\) with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height \(h\) is.

A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the faces at a point that is directly above the centre of the face at a height 3a/4 above the base. The minimum value of F for which the cube begins to topple an edge is (assume that cube does not slide)

Moment of a force of magnitude 10 N acting along positive $y$-direction at point $(2 \mathrm{~m}, 0,0)$ about the point $(0,1 \mathrm{~m}, 0)$ in $\mathrm{N}-\mathrm{m}$ is