Two  bodies with volumes V and 2V are equalized on a balance. The larger body is then immersed in oil of density = 0.9 g/cc. what must be the density of the liquid in which the smaller body simultaneously immersed so as not to disturb the equilibrium of the balance ?

Asked by Paresh | 20th Nov, 2015, 11:00: AM

Expert Answer:

Given:

V1 = V
V2 = 2 V
both have the same mass.  

Therefore, their densities are,
M1 = M2      and    d2 = ½ × d1
M2 is immersed in oil of density 0.9 g/cc
Buoyancy force on the larger body, M2 =  V2 × 0.9 × g 

let the density of the liquid in which the smaller body M1 is immersed be  d g/cc
Buoyancy force on the smaller body,  M1 =  V1 × d × g
 For the balance to remain at equilibrium,    M2 = M1

 V2 × 0.9 × g = V1 × d × g

begin mathsize 12px style straight d space equals space 0.9 space cross times space straight V subscript 2 over straight V subscript 1 space equals space 0.9 space cross times space fraction numerator 2 straight V over denominator straight V end fraction space equals space 1.8 space straight g divided by cc end style

The density of the liquid in which the smaller body simultaneously immersed is 1.8 g/cc

Answered by Priyanka Kumbhar | 20th Nov, 2015, 11:42: AM