A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of the area a floats on the surface of the liquid, covering an entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, (dr/r), is

mg/Ka

Ka/mg

Ka/3mg

mg/3Ka

Solution

mg/3Ka

$B u l k m o d u l u s, K = \frac{V o l u m e t r i c s t r e s s}{V o l u m e t r i c s t r a i n} K = \frac{m g}{a (\frac{d V}{V})} \Rightarrow \frac{d V}{V} = \frac{m g}{K a} . . . . (i) V o l u m e o f s p h e r e, V = \frac{4}{3} π R^{3} F r a c t i o n a l C h a n g e i n v o l u m e \frac{d V}{V} = \frac{3 d r}{r} . . . . (i i) U \sin g e q u (i) & (i i) \frac{3 d r}{r} = \frac{m g}{K a} ∴ \frac{d r}{r} = \frac{m g}{3 K a} (f r a c t i o n a l d e c r e m e n t i n r a d i u s)$

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Solids

Some More Questions From Mechanical Properties of Solids Chapter

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction