In the figure, the mass of a ball is 9 5 times the mass of the rod. Length of the rod is 1 m . The level of ball is the same as rod level. Find out the time taken by the ball to reach at the upper end of the rod.

Step-by-step solution

Let a 1 and a 2 be accelerations of a ball (upward) and rod (downward), respectively. Clearly, from the diagram 2 a 1 - a 2 ...(i) Now, for the ball 2 T - 9 5 m g - 9 5 m a ...(ii) and for the rod, m g - T = m a 2 ...(iii) On solving equations (i) and (iii), we get a 1 = g 29 m s - 2 ↑ (upward) a 2 = 2 g 29 m s - 2 ↓ (downward) So, acceleration of ball w.r.t rod = a 1 + a 2 = 3 g 29 Now, displacement of ball w.r.t. rod when it reaches the upper end of rod is 1 m . Using the equation of motion, s = u t + 1 2 a t 2 s