Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of length 10 m, as shown in the figure. Point mass A of mass m travelling horizontally with speed 10 ms ⁻¹ hits bob B elastically. The bob B rises h meter after the collision. Taking the acceleration due to gravity g=10 ms ⁻² and neglecting the size of the bob, the value of h is :

Step-by-step solution

Since the collision is elastic and the masses of A and B are equal, they will exchange their velocities upon collision. Velocity of bob B just after the collision, v = 10 ms ⁻¹ . By conservation of mechanical energy for bob B during its upward swing: 1 2 m v^2 = m g h Substituting the given values ( v = 10 ms ⁻¹ , g = 10 ms ⁻² ): 1 2 m (10)^2 = m 10 h 50 = 10 h h = 5 m. Since h Answer: 5