A simple pendulum is completely submerged in water. Discuss the variation in its time period. By Shourya

There will be a buoyant force on the bob.

 

So the force in the vertical direction=mg-B=Vd_sg-Vd_lg

 

the restoring torque=-V(d_s-d_l)gl?=-k?

spring factor,k=V(d_s-d_l)gl

time period=2??(inertia factor/spring factor)

=2??{ml² /V(d_s-d_l)gl}    ,m=Vd_s

=2??{d_sl_/(d_s-d_l)g}

 

a=(mg-B)/m

 

so, T=2??l/a

 

put the value of a in the above expression.