Bob B of mass m hangs initially at rest on a light string of length 10 m. Another point mass A of equal mass m strikes B horizontally at 10 m s⁻¹ in a perfectly elastic head-on collision. Bob B subsequently rises by height h. Take g = 10 m s⁻². Find h. Image
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Question

Bob B of mass m hangs initially at rest on a light string of length 10 m. Another point mass A of equal mass m strikes B horizontally at 10 m s⁻¹ in a perfectly elastic head-on collision. Bob B subsequently rises by height h. Take g = 10 m s⁻². Find h. Image

Options

G1 Physics · Accepted Answer

Step 1: For a one-dimensional elastic collision between equal masses, the initially moving mass transfers its velocity to the initially stationary mass. Step 2: Hence immediately after collision, bob B has speed v_B = 10 m s⁻¹. Step 3: As B rises, kinetic energy converts into gravitational potential energy: (1/2)mv_B² = mgh. Step 4: Cancel m and solve: h = v_B²/(2g) = 10²/(2 × 10). Step 5: h = 100/20 = 5 m (which is smaller than the maximum possible rise 2L = 20 m). Final answer: 5 m (Option C).