Question

A string of length 3$l$ is connected to a fixed cylinder whose top view is shown in figure. The string is initially slack. The other end of the string (connected to a marble) is moving at a constant velocity of 10 m/s as shown. The string will get stretched at some instant and impulsive tension occurs in the string. If hinge is exerting a force of 40000 N for 0.25 ms on the cylinder to bear up the impact of impulsive tension, then mark the correct statements. (Take string to be light, breaking tension of the string is $2\times {10}^5$ N.)

• A. The angle made by the velocity of marble with length of string when it is just stretched is 60${}^o$.
• B. The marble will move in a circular path of varying radius with constant speed of 5$\sqrt{3}$m/s, after the string is taut.
• C. To answer above two option, the volume of $\theta$ must be given.
• D. The string will break if impulse duration is less than 0.05 min.

Answer 1

Answer: (A), (B), (D)

The correct options are
A The angle made by the velocity of marble with length of string when it is just stretched is 60${}^o$.
B The marble will move in a circular path of varying radius with constant speed of 5$\sqrt{3}$m/s, after the string is taut.
D The string will break if impulse duration is less than 0.05 min.