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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 Properties of Solid and Liquid

HARD

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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}

)

EASY

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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

EASY

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

Proof resilience is related to

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

The value of

\tan θ

in the graph gives

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MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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}

)

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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:

EASY

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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?

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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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MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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,

HARD

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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)

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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

EASY

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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 Properties of Solid and Liquid

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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