Question

A spring mass system is on a horizontal plane. Spring constant is 2N/m & mass of block is 2kg. The spring is compressed by 10cm and released. A small ball is released from a height of 2m above the block on the horizontal plane. At what time should the ball be left if the block is released from the extreme position at t=0, given that the ball has to fall on the block when the speed of block is maximum?

(a) 1.57s

(b) 0.94s

(c) 0s

(d) 0.63s

Answer 1

The correct choice is (b) 0.94s

Explanation: w = √2/2 = 1. Time period of SHM = 2π/w = 2π s.                                                                                          Speed of the block will be maximum at the mean position.                                                                                  Time to reach mean position from extreme position = T/4

= 2π/4 = π/2 =1.57s.                       

Time for the small ball to fall down = √(2h/g) = √(4/9.8) = 0.63s.                                                                                                ∴ Time when it should be released                                                                                                                                                   = 1.57 – 0.63 s                                                                                                                                                                            = 0.94s.