A simple pendulum has a time period 'T' in vacuum. Its time period when it is completely immersed in a liquid of density one-eight of density of material of bob is :
Given,
Density of liquid / density of bob =dLdB=18
Time period of simple pendulum, T∝1√g
(Where, g= acceleration of gravity)
Weight in liquid = weight in vaccume – buoyancy force.
(dBV)a=(dBV)g−(dLV)g (Where, V= volume of bob)
Due to buoyancy, downward acceleration become, a=g[1−dLdB]
Time period in vacuume / time period in liquid =TT2
TT2= ⎷g[1−dLdB]g
TT2=√1−dB8.dB=√78
T2=√87T
Hence, time period in liquid is T2=√87T