A pendulum has a time period T in air. When it is made to oscillate in water its time period is 2 ~T . Then the relative density of the material of the bob of the pendulum is (neglect damping)

Step-by-step solution

The effective acceleration of a bob in water g^ =g (1- ) Here and are the density of water and the bob respectively. The time period in air is T=2 I g The time period in water is T=2 I g^ Divide equation (2) by (1), we have aligned & T^ T = I g^ g I & 2 T T = g g (1- ) & 2 = 1 1- aligned Since ( =1) aligned & 2= 1 1- 1 1- 1 = 1 2 1 = 1 2 & =2 aligned