Question

161. The bulk modulus of a spherical object is ‘B’. If it issubjected to uniform pressure ‘p’, the fractionaldecrease in radius is
(1) p/B (2) B/3p
(3) 3p/B (4) p/3B

Answer 1

Answer:

I will to answer for points sorry buddy

Answer 2

Hence, fractional decreases in radius is P/3 B

Explanation:

Volume of sphere V = 4/3 π r^3

Differentiate both sides with respect to r

dV / dr = 4π   r^2

ΔV = 4π   r^2π Δr

Dividing by, V =  4/3 π r^3

ΔV / V = 3 Δr / r

Now, we know the formula,

Bulk modulus , B = -P / Δv / v

Use ∆V/V = 3∆r/r from above derivation

B = -P/3(∆r/r)

-∆r/r = P/3 B

Hence, fractional decreases in radius is P/3B