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A solid is immerged in a liquid with half of its volume immerged in liquid .A push is given to the solid so that its start oscillating.Find time period of oscillation?  
Asked by riteshguru420 | 12 Sep, 2019, 23:47: PM
answered-by-expert Expert Answer
As shown in figure, when a partially floating object is pressed little to increase the immersion height,
 
applied force F balances the increase in upward thrust.  Hence  F = - (Δh×A)×ρl × g  ...............(1)
 
where Δh is displacement, A is area of crosssection, ρl is density of liquid and g is acceleration due to gravity.
 
equation (1) is written as ,  F = -k × Δh  ....................(2)
 
where k is force constant,  k = ( A ×ρl × g ) 
 
From eqn.(2), it can be seen that force is proportional to displacement, hence the motion is SHM.
 
angular frequency ω of SHM is given by,  ω = (k/m)1/2  , where m is mass of solid
 
ω = 2π f = (k/m)1/2
 
period  T = 1/f = 2π [ m/k ]1/2 =  2π [ m / ( A × ρl × g ) ]1/2
Answered by Thiyagarajan K | 13 Sep, 2019, 09:00: AM

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