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 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.
Solution
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#### The correct options areB After cutting the string (2) motion of centre of mass of the rod is not circularC 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 string2. 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 string2. And it will vary with the acceleration a=v2instantr. Therefore, its acceleration along the string will be 0.The acceleration of the point A perpendicular to the string1 is not zero because of the unbalanced forces along the direction.

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