Question

A uniform rod AB of mass m and length l is in equilibrium with the help of two identical inextensible strings as shown in 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.

Since after cutting the string, point A will move in a circular motion and relative to point A, CM will move in a circular motion, hence in ground frame, the motion of CM is not circular.

Since velocity of point A just after cutting the string will be 0, by $a=\frac{v^2}{r}$, its acceleration along the string will be $0$.

Due to unbalanced forces along the direction perpendicular to string, acceleration in this direction will be non zero.