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

This question was posed to me in an interview.

This is a very interesting question from Oscillations in division Oscillations of Physics – Class 11

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.