EASY

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For two different materials it is given that $Y_{1} > Y_{2}$ and $B_{1} < B_{2}$ . Here, $Y$ is Young's modulus of elasticity and $B$ , the Bulk modulus of elasticity. Then we can conclude that :

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Important Questions on Elasticity

EASY

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

Copper of fixed volume

V

is drawn into wire of length

l

. When this wire is subjected to a constant force

F,

the extension produced in the wire is

∆ l .

Which of the following graph is a straight line?

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

Young's moduli of two wires

A

and

B

are in the ratio

7 : 4

. Wire

A

2 m

long and has radius

R .

Wire

B

1.5 m

long and has radius

2 m m .

If the two wires stretch by the same length for a given load, the value of

R

is close to:

HARD

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

A steel wire of diameter

0.5 mm

and Young's modulus

2 \times 10^{11} N m^{- 2}

carries a load of mass

M

. The length of the wire with the load is

1.0 m

. A vernier scale with

10

divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count

1.0 mm

, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by

1.2 kg

, the vernier scale division which coincides with a main scale division is __________. Take

g = 10 m s^{- 2} and π = 3.2

MEDIUM

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

A steel rail of length

5 m

and area of cross section

40 {cm}^{2}

is prevented from expanding along its length while the temperature rises by

10 ° C

. If coefficient of linear expansion and Young's modulus of steel are

1.2 \times 10^{- 5} K^{- 1}

and

2 \times 10^{11} N m^{- 2}

respectively, the force developed in the rail is approximately:

MEDIUM

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

A wire is stretched such that its volume remains constant. The Poisson’s ratio of the material of the wire is:

HARD

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

A thin

1 m

long rod has a radius of

5 mm

. A force of

50 {π×10}^{3} N

is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is

0.01 mm

, which of the following statements is false?

MEDIUM

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

A rubber cord has a cross-sectional area

10^{- 6} m^{2}

and total unstretched length

0.1 m

. It is stretched to

0.125 m

and then released to project a particle of mass

5.0 g

. The velocity of projection is [Given, Young's modulus of rubber,

Y = 5 \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

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:

EASY

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

An object of mass

m

is suspended at the end of a massless wire of length

L

and area of cross-section, A. Young modulus of the material of the wire is

Y

. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

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

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 Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

EASY

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

The Young's modulus of a perfectly rigid body is

EASY

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

A bar is made up of material whose Young's modulus is

E

, Poisson's ratio

μ

and is subjected to hydrostatic pressure

p

. The fractional change in its volume

(\frac{Δ V}{V})

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

A uniformly tapering conical wire is made from a material of Young's modulus

Y

and has a normal, unextended length

L

. The radii, at the upper and lower ends of this conical wire, have values

R

and

3 R

, respectively. The upper end of the wire is fixed to a rigid support and a mass

M

is suspended from its lower end. The equilibrium extended length, of this wire, would equal:

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:

HARD

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

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to

T_{M}

. If the Young's modulus of the material of the wire is

Y

, then

\frac{1}{Y}

is equal to:
(

g =

gravitational acceleration)

For two different materials it is given that Y1> Y2 and B1< B2 . Here, Y is Young's modulus of elasticity and B , the Bulk modulus of elasticity. Then we can conclude that :

Important Questions on Elasticity

Learn and Prepare for any exam you want !

For two different materials it is given that $Y_{1} > Y_{2}$ and $B_{1} < B_{2}$ . Here, $Y$ is Young's modulus of elasticity and $B$ , the Bulk modulus of elasticity. Then we can conclude that :