Question

A ball tied to the end of a string of length 10cm is rotated with constant speed of 2m/s in a circle about the origin. Find the equation of projection of the ball on the x-axis. At t=0, the ball makes an angle of 45° with the x-axis & is travelling in anticlockwise direction.

(a) 0.1sin(20t + 3π/4)

(b) 0.1cos(20t + π/4)

(c) 10sin(20t + π/4)

(d) 10cos(20t – 3π/4)

This question was posed to me during an interview.

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

Answer 1

Correct option is (a) 0.1sin(20t + 3π/4)

Easy explanation: Let the equation of motion be: x = A sin(wt + a).                                                                                                      The amplitude is 0.1m,                                                                                                                                                              w = 2/0.1 = 20s^-1.                                                                                                                                                                     a will be either π/4 or 3π/4 since at t=0, x = A/√2.                                                                                                                                                                                                                                                                                              The ball is travelling in anticlockwise direction so its velocity of projection at t=0 should be towards the origin and therefore negative.                                                                                                                                                          v = Aw cos(wt + a).

At t=0, v is negative, so a will be 3π/4.                                                                                                                         Therefore eqn is: x = 0.1sin(20t + 3π/4)