The bob of a simple pendulum is made of a material of density (6)/(5)xx10^(3)k/gm^(3) The bob executes S.H.M in water with frequency v while the frequency of oscillation, the relationship between v and v_(0) is

The bob of a simple pendulum is made of a material of density (6)/(5)x

1.	The bob of a simple pendulum is made of a material of density (6)/(5)xx10^(3)k/gm^(3) The bob executes S.H.M in water with frequency v while the frequency of oscillation, the relationship between v and v_(0) is
Answer» `V= sqrt3v_(0)` `V= (1)/(SQRT3)v_(0)` `v=(v_(0))/(SQRT6)` `v=sqrt2v_(0)` Solution :DENSITY of water `( = 1000 kg//m^(3))` is 5/6 of the density of the bob, So, the effective acceleration due to gravity when the bob is in water decreaes (due to upthrust) from g to `g. = g - (5g)/(6) = (g)/(6)` In air, `v_(0) = (1)/(2pi) sqrt((g)/(l))` In water, `v = (1)/(2pi) sqrt((g.)/(l))` Dividing both expressions, we get `(v)/(v_(0)) = sqrt((g.)/(g)) = sqrt((g/6)/(g)) = sqrt((1)/(6))` ` v = (v_(0))/(sqrt(6))`