Question

A uniform rod AB of mass m and length $\ell$ is in equilibrium with the help of two identical inextensible strings as shown in the figure. Choose the correct option (s)

• A. After cutting the string (2) motion of centre of mass of the rod is circular
• B. After cutting the string (2) motion of centre of mass of the rod is not circular
• C. Just after cutting the string (2) the acceleration of point A along the string (1) is zero.
• D. Just after cutting the string (2) the acceleration of point A perpendicular to the string (1) is not zero.

Answer 1

Answer: (B), (C), (D)

The correct options are
B After cutting the string (2) motion of centre of mass of the rod is not circular
C Just after cutting the string (2) the acceleration of point A along the string (1) is zero.
D Just after cutting the string (2) the acceleration of point A perpendicular to the string (1) is not zero.

The point $A$ will move in a circular motion after cutting the string$2$. But, relative to the point $A$, the center of mass will also move in a circular motion, keeping $A$ its center. Therefore in the ground frame, the motion of the center of mass will not be circular.

The instantaneous velocity of the point $A$ will be 0 after cutting the string$2$. And it will vary with the acceleration $a=\frac{{v^2}_{\text{instant}}}{r}$. Therefore, its acceleration along the string will be $0$.

The acceleration of the point $A$ perpendicular to the string$1$ is not zero because of the unbalanced forces along the direction.