# 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

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 Fb (or upward thrust) imparted by the liquid on the cube given as Fb = 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 + Fb = mg
x = (mg-Fb) /k
= (mg-Vdg) /k , Where V = (m/D)
x =mg/k(1-d/D)

## Author: Rajesh Jha

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