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For an ideal liquid, bulk modulus is infinite and shear modulus is zero.

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Important Questions on Elasticity

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 $g = 9.8 {m s}^{- 2} .$

MEDIUM

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

A particle of mass

1 kg

is moving in SHM with a path length of

0.01 m

and frequency of

50 Hz

. The maximum force in newton, acting on the particle is

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 :

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 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:

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 wrong statement in the following is

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

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

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})

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:

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 :

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}

)

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 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}

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

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

1 %

? (Bulk modulus

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

)

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

One end of a horizontal thick copper wire of length

2 L

and radius

2 R

is welded to an end of another horizontal thin copper wire of length

L

and radius

R

. When the arrangement stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

For an ideal liquid, bulk modulus is infinite and shear modulus is zero.

Important Questions on Elasticity

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