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If the Young's modulus of the material of a wire is numerically equal to ten times the stress applied to a wire of length $l$ , then the change in the length of the wire is

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Important Questions on Elasticity

MEDIUM

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

One end of a slack wire (Young's modulus,

Y

, length,

L

and cross-sectional area,

A

) is clamped to a rigid wall and the other end to a block (mass

m

) which rests on a smooth horizontal plane. The block is set in motion with a speed,

v

. What is the maximum distance the block will travel after the wire becomes taut?

EASY

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

A rubber cord of density

d,

Young's modulus

Y

and length

L

is suspended vertically. If the cord extends by a length

0.5 L

under its own weight, then

L

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:

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:

EASY

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

In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :

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

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:

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:

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 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?

EASY

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

The value of

\tan θ

in the graph gives

Question Image

MEDIUM

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

A boy’s catapult is made of rubber cord which is

42 c m

long, with

6 m m

diameter of cross-section and of negligible mass. The boy keeps a stone weighing

0.02 k g

on it and stretches the cord by

20 c m

by applying a constant force. When released, the stone flies off with a velocity of

20 m s^{- 1}

. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:

MEDIUM

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

The length of elastic string obeying Hooke's law is

l_{1}

metres when the tension is

4 N

and

l_{2}

metres when the tension is

5 N

. The length in metres when the tension is

9 N

is,

EASY

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

When a block of mass

M

is suspended by a long wire of length

L

, the length of the wire becomes

(L + l) .

The elastic potential energy stored in the extended wire is

MEDIUM

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

The elastic limit of brass is

379 M P a

. The minimum diameter of a brass rod if it is to support a

400 N

load without exceeding its elastic limit will be

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?

MEDIUM

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

A metal rod of length

L

and cross-sectional area

A

is heated through

T ° C

. What is the force required to prevent the expansion of the rod lengthwise?

[Y

= Young's modulus of the material of rod,

α =

coefficient of linear expansion

]

MEDIUM

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

The decrease in length of a metal bar of length

L

and cross-sectional area

A

when compressed with a load

M

along its length is (

Y =

Young's modulus of the material of metal bar)

EASY

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

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area

A

and the second wire has cross-sectional area

3 A .

If the length of the first wire is increased by

∆ l

on applying a force

F,

how much force is needed to stretch the second wire by the same amount?

If the Young's modulus of the material of a wire is numerically equal to ten times the stress applied to a wire of length l, then the change in the length of the wire is

Important Questions on Elasticity

Learn and Prepare for any exam you want !

If the Young's modulus of the material of a wire is numerically equal to ten times the stress applied to a wire of length $l$ , then the change in the length of the wire is