Question

Figure below shows two blocks of masses 5 kg and 2 kg placed on a frictionless surface and connected with a spring. An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one. Deduce (a) velocity gained by the centre of mass and (b) the separate velocities of the two blocks in the centre of mass coordinates just after the kick.

• A. 10 m/s, 14 m/s, 10 m/s
• B. 10 m/s, 4 m/s, 10 m/s
• C. 10 m/s, 4 m/s, -10 m/s
• D. 10 m/s, 10 m/s, 10 m/s

Answer 1

The correct option is C 10 m/s, 4 m/s, -10 m/s

a. Velocity of centre of mass is
$v_{CM}=\frac{5\times 14+2\times 0}{5+2}=10m/s$
b. Due to the kick on the 5 kg block, it starts moving with a velocity 14 m/s immediately, but due to inertia, 2 kg block remains at rest, at that moment. Thus, velocity of 5 kg block with respect to centre of mass is $v_1=14-10=4m/s$, and velocity of 2 kg block with respect to centre of mas is $v_2=0-10=–10m/s$.