A cube of mass `m` and density `D` is suspended from a point `P` by a spring of stiffness `k`. The system is kept inside a beaker filled with a liquid of density `d`. The elongation in the spring, assuming `D gt d`, is :

Options

A. `(mg)/k (1-d/D)`
B. `(mg)/1 (1-D/d)`
C. `(mg)/k (1+d/D)`
D. None of these

Explanation

The cube is in equilibrium under the following three forces ,
spring force kx , where x = elongation of the spring ,
gravitional force w , weight of the cube = mg
buoyant force `F_(b)` ( or upward thrust ) imparted by the liquid on the cube given as `F_(b) = Vdg` where V = volume of the immersed portion of the cube equilibrium of the cube , ` kx + F_(b) = mg`
`rArr x = (mg -F_(b))/(k) = (mg- Vdg)/k ` where V = volume he immersed portion of the cube , For complete immersion , V = volume of the cube
For equilibrium of the cube , ` kx + F_(b) = mg`
` rArr = (mg-F_(b))/k = (mg-Vdg)/k ` Where V = (m/D)
` rArr x = (mg)/k (1- d/D)`
Hence (A) is correct