A cube of mass m and density D is suspended from the point P by a spring of stiffness k. The system is kept inside…..

Q: A cube of mass m and density D is suspended from the 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 > d, is

(A) mg/k(1-d/D)

(B) mg/k(1-D/d)

(C) mg/k(1+d/D)

(D) None of these.

Solution:

The cube is in equilibrium under the following three forces,

(a) spring force kx, where x = elongation of the spring,

(b) gravitational force w, weight of the cube = mg

(c) 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. For complete immersion, V = volume of the cube.

For equilibrium of the cube, kx + F_b = mg

x = (mg-F_b) /k

= (mg-Vdg)/k , Where V = (m/D)

x = mg/k(1-d/D)