When a pressure of 100 atmosphere is applied on a spherical ball of rubber, then its volume reduces to 0.01 %. The bulk modulus of the material of the rubber in dyne cm -2 is

Question

When a pressure of 100 atmosphere is applied on a spherical ball of rubber, then its volume reduces to 0.01 %. The bulk modulus of the material of the rubber in dyne cm -2 is (A) 10 × 1012 (B) 100 × 1012 (C) 1 × 1012 (D) 20 × 1012

Tardigrade Admin · Accepted Answer

We know that, 1 atm =105 Nm -2 ∴ 100 atm =107 Nm -2 and Δ V=0.01 % V ∴ (Δ V/V)=0.0001 |B|=(p/Δ V / V)=(107/0.0001) =1 × 1011 Nm -2 =1 × 1012 dyne cm -2 [∵ 1 N =105. dyne ]

Q. When a pressure of 100 atmosphere is applied on a spherical ball of rubber, then its volume reduces to $0.01%$ . The bulk modulus of the material of the rubber in dyne $c m^{- 2}$ is

$10 \times 1 0^{12}$

$100 \times 1 0^{12}$

$1 \times 1 0^{12}$

$20 \times 1 0^{12}$

We know that, $1$ atm $= 1 0^{5} N m^{- 2}$
$∴ 100 a t m = 1 0^{7} N m^{- 2}$
and $Δ V = 0.01% V$
$∴ \frac{Δ V}{V} = 0.0001$
$∣ B ∣ = \frac{p}{Δ V / V} = \frac{1 0 ^{7}}{0.0001}$
$= 1 \times 1 0^{11} N m^{- 2}$
$= 1 \times 1 0^{12}$ dyne $c m^{- 2}$
$[∵ 1 N = 1 0^{5}$ dyne $]$

Q. When a pressure of 100 atmosphere is applied on a spherical ball of rubber, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber in dyne cm−2 is

10×1012

100×1012

1×1012

20×1012