The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M. Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its center. The magnitudes of the acceleration experienced by the blocks is ________ (assume no slipping of string on pulley).

A uniform rod of mass $m$ and length $l$ suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is $\_\_\_\_$ . $(g$ acceleration due to gravity)

A rod of linear mass density 'λ' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is.

Which of the following are correct expression for torque acting on a body?

A. $\vec{\tau}=\vec{r} \times \vec{L}$

B. $\vec{\tau}=\frac{d}{d t}(\vec{r} \times \vec{p})$

C. $\vec{\tau}=\vec{r} \times \frac{d \vec{p}}{d t}$

D. $\vec{\tau}=I \vec{\alpha}$

E. $\vec{\tau}=\vec{r} \times \vec{F}$

( $\vec{r}=$ position vector; $\vec{p}=$ linear momentum; $\vec{L}=$ angular momentum; $\vec{\alpha}=$ angular acceleration; $I=$ moment of inertia; $\vec{F}=$ force; $t=$ time)

Choose the correct answer from the options given below: