Two blocks A and B of masses 10 kg and 5 kg are on a frictionless table. Block A moves at 3 m/s toward block B, which is initially at rest and has a spring of force constant 3000 N/m attached to it as shown in the original figure. At maximum compression, both blocks move together instantaneously. The spring compression is:

Question

G1 Physics · Accepted Answer

At maximum compression, the two blocks have the same instantaneous velocity because their relative speed is zero. Conserve linear momentum: 10(3) + 5(0) = (10+5)V. Thus, V = 30/15 = 2 m/s. Initial kinetic energy: Kᵢ = ½(10)(3²) = 45 J. Kinetic energy of both blocks at maximum compression: K c m K_cm K c ​ m = ½(15)(2²) = 30 J. The decrease in kinetic energy is stored in the spring: ½kx² = 45-30 = 15 J. Therefore, ½(3000)x² = 15 ⇒ 1500x² = 15 ⇒ x² = 0.01 ⇒ x = 0.1 m. Correct option: A.