Question

A 10N force  is uniformly distributed over the surface of a sphere of radius 20cm. The force at each point acts inward along the normal at that point. Find the fractional change in volume if the compressibility of the sphere is 10^-11m^2/N.

(a) 3*10^-10

(b) 1.5*10^-11

(c) 1.98*10^-10

(d) 2*10^-11

I have been asked this question in an online quiz.

My query is from Solids Mechanical Properties topic in portion Mechanical Properties of Solids of Physics – Class 11

Answer 1

Right choice is (c) 1.98*10^-10

Best explanation: Bulk Modulus ‘B’ is defined as -P / (ΔV/V). And B is the reciprocal of compressibility.

∴ B = 1/10^-11= 10^11N/m^2.

 ΔV/V = P/B.

P = 10/(4π*0.04)

∴ ΔV/V = -P/B = – 10/(4π*0.04*10^11) = 1.98*10^-10.