EASY

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Lengths L, 2L and 3L and radii R, 2R and 3R of three wires of same material (Young's modulus Y) respectively which are joined end to end with weight $ω$ is suspended as shown below. Find the elastic ${(P . E)}_{s y s t e m}$ neglecting the self weight

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Important Questions on Elasticity

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{- 4}$ is _____ $kJ m^{- 3}$ . Assume that material is elastic upto the linear strain of $5 \times 10^{- 4}$ .

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EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

A wire of Young's modulus

Y

is subjected to a stress

S

. The elastic potential energy per unit volume of the wire is given by

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

If $S$ is stress and

Y

is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

Proof resilience is related to

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

A wire of length

L

and area of cross section

A

is made of material of Young’s modulus

Y

. It is stretched by an amount

x

. The work done in stretching the wire is

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

S

is the stress and

Y

is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

What is the elastic potential energy stored in a stretched steel wire of length

4 m .

The wire is stretched through

4 mm

and consists of cross-sectional area of

8 {mm}^{2} .

(Young's modulus of steel

= 2.0 \times 10^{11} N m^{- 2}

)

HARD

Physics>Mechanics>Elasticity>Elastic Potential Energy

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>Elastic Potential Energy

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is

1 : 4,

the ratio of their diameters is:

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

Consider a metallic wire of length

10 m

. An external force applied results in an elongation of

5 mm

. What is the potential energy stored per unit volume
[Young's modulus of wire

Y = 16 \times 10^{10} N m^{- 2}

]

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

The area of cross section of the rope used to lift a load by a crane is

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

. The maximum lifting capacity of the crane is

10

metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be
(take

g = 10 {ms}^{- 2}

)

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

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

HARD

Physics>Mechanics>Elasticity>Elastic Potential Energy

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)

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

An aluminium rod with Young’s modulus

Y = 7.0 \times 10^{10} N m^{- 2}

undergoes elastic strain of

0.04 %

. The energy per unit volume stored in the rod in

SI

unit

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

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>Elastic Potential Energy

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>Elastic Potential Energy

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>Elastic Potential Energy

A stone of mass

20 g

is projected from a rubber catapult of length

0.1 m

and area of cross section

10^{- 6} m^{2}

stretched by an amount

0.04 m .

The velocity of the projected stone is

m s^{- 1} .

(Young's modulus of rubber

= 0.5 \times 10^{9} N m^{- 2}

)

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

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>Elastic Potential Energy

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?

Lengths L, 2L and 3L and radii R, 2R and 3R of three wires of same material (Young's modulus Y) respectively which are joined end to end with weight ω is suspended as shown below. Find the elastic P.Esystem neglecting the self weight

Important Questions on Elasticity

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Lengths L, 2L and 3L and radii R, 2R and 3R of three wires of same material (Young's modulus Y) respectively which are joined end to end with weight $ω$ is suspended as shown below. Find the elastic ${(P . E)}_{s y s t e m}$ neglecting the self weight