Paragraph: The time-period of a simple pendulum performing simple harmonic motion, having length is given T =2 ~g This formula holds good if following conditions are satisfied. (i) String is massless and extensible. (ii) Bob is a point mass. (iii) Angular displacement about mean position is very small, and (iv) Length of string is very small as compared to the radius of earth ( R _ e ) . Question: If the bob is a hol

Step-by-step solution

When the bob is hollow _ eq = 2 R ^2 3( + R ) +( L + R ) T ₁=2 _ eq g =2 2 R ^2 3( ~L + R ) +( L + R ) g when filled with water, total energy aligned & E= 1 2 m_w ^2(L+R)^2+ 1 2 M ^2(L+R)^2+ 1 2 2 3 M ^2 R^2+ (M_w+M ) g(L+R)(1- ) & d E d t =0 d^2 d t^2 + [ g(L+R) 2 3 M R^2 (M+M_w ) +(L+R)^2 ] =0 T₂=2 2 3 ( M M+M_w ) R^2 L+R +(L+R) g aligned Therefore T ₂ T ₁ ~T ₁ ~T ₂ 1OR Water will not rotate therefore system has more translation KE, hence more average speed for same amplitude. So time period will decrease.