A body is dropped from height h₁ and rebounds to height h₂. If the ratio of speeds just before and just after hitting the ground is 4, the percentage loss in kinetic energy is x/4. Find x.
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 2 Evening Shift

Question

A body is dropped from height h₁ and rebounds to height h₂. If the ratio of speeds just before and just after hitting the ground is 4, the percentage loss in kinetic energy is x/4. Find x.

G1 Physics · Accepted Answer

Let speed just before impact be u and just after rebound be v. Given: u/v = 4 Therefore, v = u/4 Kinetic energy before impact: K₁ = (1/2)mu² Kinetic energy after impact: K₂ = (1/2)m(u/4)² = K₁/16 Fractional loss: (K₁−K₂)/K₁ = 1 − 1/16 = 15/16 Percentage loss: (15/16)×100 = 93.75% = 375/4 % Hence x = 375. Final value: 375