EASY

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Why does bulk modulus of elasticity and pressure have same units?

Important Questions on Elasticity

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

The bulk modulus of a liquid is

3 \times 10^{9} N m^{- 2}

The pressure required to reduce the given volume of this liquid by

1 %

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

The normal density of a material is

ρ

and its bulk modulus of elasticity is

K

. The magnitude of increase in density of material, when a pressure

P

is applied uniformly on all sides, will be :

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

When a rubber ball is taken to a depth of _______

m

in deep sea, its volume decreases by

0.5 %

(The bulk modulus of rubber

= 9.8 \times 10^{8} N m^{- 2}

Density of sea water

= 10^{3} kg m^{- 3}

g = 9.8 m s^{- 2}

)

HARD

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

The compressibility of a substance is the reciprocal of ____.

HARD

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

A bottle has an opening of radius

a

and length

b

. A cork of length

b

and radius

(a + ∆ a)

where

(∆ a ≪ a)

, is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is

B

and the coefficient of friction between the bottle and cork is

μ

, then the force needed to push the cork into the bottle is

Question Image

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

The radius of a sphere is found to have reduced by

0.01 %

, when measured at a depth

' H'

of the sea. If the bulk modulus of elasticity of the material of sphere is

4 \times 10^{10} N m^{- 2}

and density of water is

1000 kg m^{- 3}

, find the value of

H

' (use

g = 10 m s^{- 2})

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

An object is located at $2 km$ beneath the surface of the water. If the fractional compression $\frac{Δ V}{V}$ is $1.36 %$ , the ratio of hydraulic stress to the corresponding hydraulic strain will be ______[Given: density of water is $1000 kg m^{- 3}$ and $g = 9.8 {m s}^{- 2} .$

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

A certain pressure '

P

' is applied to

1

litre of water and

2

litre of a liquid separately. Water gets compressed to

0.01 %

whereas the liquid gets compressed to

0.03 %

. The ratio of Bulk modulus of water to that of the liquid is

\frac{3}{x}

. The value of

x

is ______.

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

A cubical solid aluminum

(bulk modulus = - V \frac{d P}{d V} = 70 GPa)

block has an edge length of

1 m

on the surface of the earth. It is kept on the floor of a

5 km

deep ocean. Taking the average density of water and the acceleration due to gravity to be

10^{3} kg m^{- 3}

and

10 m s^{- 2}

, respectively, the change in the edge length of the block in

mm

is ________.

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

What is the pressure required to reduce the given volume of water by

1 %

? (Bulk modulus

(K) = 2 \times 10^{8} N m^{- 2}

)

HARD

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

Define Young’s modulus.

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

The bulk modulus of a liquid is

3 \times 10^{10} {Nm}^{- 2}

. The pressure required to reduce the volume of liquid by

2 %

is :

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

A body is subjected to stress resulting in the change in volume of the body. The stress must be

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

A swimming pool has a depth of

22 m

and area

700 m^{2}

. Calculate fractional change

\frac{Δ v}{v}

of water at the bottom of the swimming pool. Given that the bulk modulus of water is

2.2 \times 10^{9} {Nm}^{- 2}, g = 10 m s^{- 2}

, and density of water

1000 kg m^{- 3}

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

A load of mass

M kg

is suspended from a steel wire of length

2 m

and radius

1.0 mm

in Searle's apparatus experiment. The increase in length produced in the wire is

4.0 mm .

Now the load is fully immersed in a liquid of relative density

2 .

The relative density of the material of load is

8 .

The new value of increase in length of the steel wire is:

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

Pressure for polytropic process $P$ varies with volume $V$ as $P = a V^{- 3}$ , Find out the bulk modulus.

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

The wrong statement in the following is

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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 area

a

floats on the surface of the liquid, covering 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

(\frac{d r}{r})

, is:

HARD

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

An external pressure

P

is applied on a cube at

0 ° C

so that it is equally compressed from all sides.

K

is the bulk modulus of the material of the cube and

α

is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

Why does bulk modulus of elasticity and pressure have same units?

Important Questions on Elasticity

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