GATE 2020 ME (ME2) – Question 50
A rigid 10 kg block at 2 m/s travels 1 m on a frictionless horizontal surface and strikes a stationary 30 kg block. They stick and travel another 0.25 m before contacting a massless buffer attached to a fixed wall by a 10⁵ N/m linear spring. Find maximum spring deflection (cm), to two decimals.
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Correct answer: .98 to 1.02
Explanation
Momentum during the inelastic impact gives shared speed10(2)/(10+30)=0.5 m/s. Remaining kinetic energy is(1/2)(40)(0.5²)=5 J. Set5=(1/2)(100000)x², givingx=0.01 m=**1.00 cm**. Energy is not conserved during impact, only during subsequent spring compression.