A uniform bar of length $L$ hinged at one end is released from horizontal position so as to fall under gravity. The initial angular acceleration of the rod will be

A uniform bar of mass $\mathrm{m}$ is being moved on a smooth horizontal plane by applying a constant horizontal force $F$ acting at the lowest point. If the rod translates making a constant angle $\theta$ with vertical, the value of $F$ must be

A disc of radius $R$ has linear velocity $v$ and angular velocity $\omega$ as shown in the figure. Given $v=R\omega$. Find speed of points $A,B,C,D$ on the disc.

A wheel rolls purely on ground. If the velocity of a point '$P$' as shown on periphery of a body has a velocity equal to the velocity of the centre of mass of the body. Then $\theta =$?

A solid circular disc $\left(m,R\right)$ translates with $v_0$ and rotates with ${\omega }_0=\frac{2v_0}{R}$, at $t=0$. Because of friction, pure rolling starts at $t=t_0$. The coefficient of friction is ${\mu }_k$.

Find $t_0$.

A solid circular disc $\left(m,R\right)$ translates with $v_0$ and rotates with ${\omega }_0=\frac{2v_0}{R}$, at $t=0$. Because of friction, pure rolling starts at $t=t_0$. The coefficient of friction is ${\mu }_k$.

Find velocity of centre of disc at $t=t_0$.

A solid cylinder rolls without slipping down a rough inclined plane without slipping as shown in figure. Choose the correct statement from the following.

A cylindrical rod of mass $M$, length $L$and radius $R$ has two cords wound around it whose ends are attached to the ceiling as shown. The rod is held horizontally with the two cords vertical. When the rod is released, cords unwind the rod rotates. Find tension in the cords as they unwind.