Question

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. $\frac { \mathrm { mg } } { \mathrm { k } } \left( 1 - \frac { \mathrm { d } } { \mathrm { D } } \right)$
• B.
• C.
• D. None of these.

Answer 1

Answer: (A)

$\frac { \mathrm { mg } } { \mathrm { k } } \left( 1 - \frac { \mathrm { d } } { \mathrm { D } } \right)$

Answer 2

The cube is in equilibrium under three forces as,

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

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

(3) buoyant force (or upward thrust) imparted by the

liquid on the cube given as $\mathrm { F } _ { 0 } = \mathrm { Vdg }$ where V = volume of

the immersed portion of the cube. For complete immersion,

V = volume of the cube.For equilibrium of the cube,

kx + = mg

⇒ where V = (m/D)

⇒