Question

If the weight of a body in vacuum is w and `w_(1)` and `w_(2)` are weights when it is immersed in a liquid of specific gravity `rho_(1)` and `rho_(2)` respectively, then find the relation among `w,w_(1)and w_(2)`
A. `w=(w_(1)rho_(2)+w_(2)rho_(1))/(w_(1)+w_(2))`
B. `w=(w_(1)rho_(2)-w_(2)rho_(1))/(rho_(2)-rho_(1))`
C. `w=(w_(1)rho_(2)+w_(2)rho_(1))/(rho_(1)+rho_(2))`
D. `(omega^(2))/(2gr^(2))`

Answer 1

(b) Loss in wight of liquid of density `rho_(1)=(w-w_(1))` kg. if V is the volume of the body. Then
`vp_(1)=w-w_(1)rArrV=(w-w_(1))/(rho_(1))`
Similarly, `vp_(2)=w-w_(2)rArrV=(w-w_(2))/(rho_(2))`
`(w-w_(1))/(rho_(1))=(w-w_(2))(rho_(2))`
`w=(w_(1)rho_(2)-w_(2)rho_(1))/(rho_(2)-rho_(1))`