Question

Two blocks of masses m and 2m are connected by a compressed spring with a string as shown in figure. The spring has an initial compression of X = 1m. The spring constant is K = 6N/m. Whole system is moving towards right with speed 1m/s. Now if the string is cut, then (Take m = 1kg and neglect friction)

(A) When m is having maximum speed, the energy stored in the spring will be 6 J.

(B) The minimum speed attained by 2m is zero.

(C) When m is having maximum speed, the energy stored in the spring will be 3 J.

(D) The maximum speed attained by m is 3 m/s.

Answer 1

Correct option: (B, D)

Explanation:

m will attain maximum speed when spring will be in its natural length.

mV₁ + 2mV₂ = 3m (1)

V₁ + 2V₂ = 3 .........(1)

from conservation of energy

1/2 (3m)(1)² + 1/2  k x² = 1/2  mV₁ ² + 1/2 2mV₂ ² .........(2)