A simple pendulum has a time period T when oscillating in air. When the pendulum bob is completely immersed in water, its time period becomes 2 T . If the density of water is 1000 kg/m ^3 and viscous forces are neglected, the density of the material of the pendulum bob is

Step-by-step solution

The time period of a simple pendulum in air is given by: T = 2 l g When immersed in a liquid, the effective acceleration due to gravity g_ eff is reduced due to buoyancy: g_ eff = g (1 - _w _b ) where _w is the density of water and _b is the density of the bob. The new time period is: T' = 2 l g_ eff Given that T' = 2 T , we have: 2 l g_ eff = 2 (2 l g ) Squaring both sides: l g_ eff = 2 ( l g ) g_ eff = g 2 Equating this to the expression for g_ eff : g (1 - _w _b ) = g 2 1 - 1000 _b = 1 2 1000 _b = 1 2 _b = 2000