A ball falling in a lake depth 200 m shows a decrease of 0.1 % in its volume at the bottom then the bulk modulus of the material of the ball is

$19.6 \times 10^{8} N / m^{2}$

$19.2 \times 10^{7} N / m^{2}$

$24 \times 10^{9} N / m^{2}$

$24 \times 10^{5} N / m^{2}$

Solution

$19.6 \times 10^{8} N / m^{2}$

The pressure exerted by water on the ball $p = hρg$

Given:- $ρ$ = $1000 \frac{kg}{m^{3}}$ (density of water) ,

h=200m

p= $10^{3}$ $\times$ 200 $\times$ 9.8=19.6 $\times 10^{5}$

$\frac{∆ V}{V} = 0.1 %$ = $\frac{0.1}{100}$

Bulk modulus B= $\frac{- p}{\frac{∆ V}{V}} =$ $\frac{hρg}{\frac{∆ V}{V}}$ = $\frac{19.6 \times 10^{5}}{0.1 \times 10^{- 2}}$

The negative sign indicates the fact that with an increase in pressure, a decrease in volume occurs.If p is positive, ∆V is negative.Thus for a system in equilibrium, the value of bulk modulus B is always positive. So B is positive

B =19.6 $\times 10^{8} \frac{N}{m^{2}}$

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Mechanical Properties Of Fluids

A ball falling in a lake depth 200 m shows a decrease of 0.1 % in its volume at the bottom then the bulk modulus of the material of the ball is

$19.6 \times 10^{8} N / m^{2}$

$19.2 \times 10^{7} N / m^{2}$

$24 \times 10^{9} N / m^{2}$

$24 \times 10^{5} N / m^{2}$

Some More Questions From Mechanical Properties of Fluids Chapter

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For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

A ball falling in a lake depth 200 m shows a decrease of 0.1 % in its volume at the bottom then the bulk modulus of the material of the ball is 19.6×108 N/m2 19.2×107N/m2 24×109 N/m2 24×105 N/m2

Some More Questions From Mechanical Properties of Fluids Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A ball falling in a lake depth 200 m shows a decrease of 0.1 % in its volume at the bottom then the bulk modulus of the material of the ball is

$19.6 \times 10^{8} N / m^{2}$

$19.2 \times 10^{7} N / m^{2}$

$24 \times 10^{9} N / m^{2}$

$24 \times 10^{5} N / m^{2}$