A bob B of mass m hangs at rest vertically from the ceiling by a massless string of length 10 m. A point mass A of mass m travelling horizontally with speed 10 ms⁻¹ hits bob B elastically. The bob B rises h metre after the collision. Taking g=10 ms⁻² and neglecting the size of the bob, the value of h is:

Solution & Explanation

Equal masses, one-dimensional elastic collision. Key result: in a head-on elastic collision between two equal masses where one is initially at rest, the two simply exchange velocities. So A stops and B moves off with the full speed v = 10 m s⁻¹. Now B swings up on the string; mechanical energy is conserved as it rises to height h: (1/2) m v² = m g h. The mass cancels: h = v²/(2g). Substitute v = 10 m s⁻¹, g = 10 m s⁻²: h = (10²)/(2×10) = 100/20 = 5 m. So h = 5 m, matching option C. (The string is 10 m, long enough to permit a 5 m rise, so the bob stays on the string throughout.)