Question

Two blocks of mass 3 kg and 6 kg respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant k=200 N/m. Initially the spring is unstretched. The indicated velocities are impacted to the blocks. Find the maximum extension of the spring.

Answer 1

Correct option is (1)

Explanation:

At maximum extension velocity of both the blocks will be same. Let v be the common velocity of the blocks (towards right). From conservation of linear momentum.

(3+6)v=6×2−3×1=9
or v=1m/s
Now let x be the maximum extension in the spring.
From conservation of mechanical energy
1/2 x (3)(1)²+1/2 x (6)(2)²=2(200)x²+1/2 x (9)(1)²
or 3+24=200x²+9
or x=√(18/200)
or x=0.3 m
x=30 cm