A ball (1 kg) hangs from a thread 1.50 m long in a frictionless trolley (4 kg). A 1 kg shell moving at 6 m s⁻¹ sticks to the ball. If maximum pendulum angular deflection is θₘₐₓ, find 10 sinθₘₐₓ (g = 10 m s⁻²). [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A ball (1 kg) hangs from a thread 1.50 m long in a frictionless trolley (4 kg). A 1 kg shell moving at 6 m s⁻¹ sticks to the ball. If maximum pendulum angular deflection is θₘₐₓ, find 10 sinθₘₐₓ (g = 10 m s⁻²). [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — The 1 kg shell sticks to 1 kg ball, giving combined mass 2 kg immediately after impact. Horizontal momentum during impact gives their speed 6/2 = 3 m s⁻¹. Step 2 — After collision, total horizontal momentum 6 kg m s⁻¹ of combined shell+ball+trolley (mass 6 kg) is conserved. At maximum angle all have common horizontal velocity 6/6=1 m s⁻¹. Step 3 — Kinetic energy just after collision is (1/2)2×3²=9 J; at maximum angle the common motion has (1/2)6×1²=3 J. So 6 J becomes gravitational ene…