Question

The spring block system lies on a smooth horizontal surface. The free endof the spring is being pulled towards right with constant speed `v_(0) = 2m//s`. At `t = 0 sec`, the spring of constant `k = 100 N//cm` is unsttretched and the block has a speed `1 m//s` to left. The maximum extension of the spring is.
.
A. 2 cm
B. 4 cm
C. 6 cm
D. 8 cm

Answer 1

Correct Answer - C
In the frame (inertial w.r.t. earth) of free end of spring, the initial velocity of block is `3 m//s` to left and the spring unstreched.

Applying conservation of energy between initial and maximum extension state.
`(1)/(2) mv^(2) = (1)/(2) kA^(2)` or `A = sqrt((m)/(k)) v= sqrt((4)/(10,000)) xx 3 = 6 cm`.