Question

A particle is kept fixed on a turntable rotating uniformly. As seen from the ground the particle goes in a circle, its speed is 20 cm/s and acceleration is 20 cm/s ². The particle is now shifted to a new position to make the radius half of the original value. The new values of the speed and acceleration will be
(a) 10 cm/s, 10 cm/s ² (b) 10 cm/s, 80 cm/s ² (c) 40 cm/s, 10 cm/s ² (d) 40 cm/s, 40 cm/s ².

Answer 1

(a) 10 cm/s, 10 cm/s ² 

Explanation: 

Velocity of the particle in a circular motion is equal to ωr , so if ω is constant the velocity is proportional to the radius. Here the particle is kept at half radius therefore velocity will be half ie = 10 cm/s. 

Similarly acceleration is ω²r , here too, ω² is constant, so acceleration is also proportional to 'r'. In this case too, making radius half will make acceleration half ie = 10 cm/s².