The metallic bob of simple pendulum has the relative density 5 . The time period of this pendulum is 10 s . If the metallic bob is immersed in water, then the new time period becomes 5 x s . The value of x will be _____ .

Step-by-step solution

When the bob is immersed in water its effective weight is m g ' = m g - F B , where, F B is buoyant force. Then, g ' = m g - F B m = ρ B Vg - ρ W Vg ρ B V = ρ B - ρ w ρ B g = 5 - 1 5 × g = 4 5 g Now, time period of simple pendulum is given by T = 2 π l g Thus, the ratio T ' T = g g ' = g 4 5 g = 5 4 ⇒ T ' = T 5 4 = 10 2 5 Thus, the new time period is T ' = 5 5   s . Hence, value of x = 5 .