A fluid of volume 1 . 5 × 10 - 3 m 3 , when subjected to a pressure change of 5 . 0 × 10 6 Nm - 2 has its volume reduced by 3 . 0 × 10 - 7 m 3 . Find the coefficient of bulk modulus of the fluid.

Given: Volume of fluid = 1 . 5 × 10 - 3 m 3 Change in pressure = 5 . 0 × 10 - 6 N / m 2 = ρ Volume reduced = 3 . 0 × 10 - 7 m 3 To find, Bulk modulus of fluid We know that, Bulk modulus = c h a n g e i n p r e s s u r e v o l u m e s t r a i n Bulk modulus = ρ ϑ / v = ρ v ϑ Bulk modulus = 5 × 10 6 N / m 2 × 1 . 5 × 10 - 3 m 3 3 . 0 × 10 - 7 m 3 Bulk modulus = 2 . 5 × 10 10 N / m 2

A wire of length 1 . 0 m bas area of cross-section 0 . 1 cm 2 . The Young's modulus of material of the wire is 2 . 5 × 10 11 Nm - 2 and coefficient of linear thermal expansion is 2 × 10 - 5 ° C - 1 . The wire is clamped between two rigid supports and its temperatures is decreased by 10 ° C . Calculate the tension developed in it.

Given: Length of wire = 1 . 0 m area of cross-section = 0 . 1 cm 2 = 0 . 1 × 10 - 4 m 2 Y w i r e = 2 . 5 × 10 11 N / m 2 Coefficient of linear expression α = 2 × 10 - 5 ° C - 1 Temperature (decreased) = 10 ° C To find, Tension developed in wire using the relation b w change in length of wire ∆ L and coefficient of l i n e a r e x p r e s s i o n α ∆ L = α L ∆ t ∆ L = 2 × 10 - 5 × 1 × 10 m = 20 × 10 - 5 m We know that Y = F L A ∆ L F = Y A ∆ L L = 2 . 5 × 10 11 × 0 . 1 × 10 - 4 × 20 × 10 - 5 1 N F = 500 N

E M B I B E

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>NUMERICALS>Q 19

HARD

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IMPORTANT

Earn 100

A brass rod of length and area of cross-section $2 {cm}^{2}$ is compressed by a force of $5 kg - wt$ along its length. Determine the increase in the length of the rod. Young's modulus of brass is $1.4 \times 10^{11} N m^{- 1}$ .

Important Questions on Elasticity

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>NUMERICALS>Q 20

A fluid of volume

1.5 \times 10^{- 3} m^{3}

, when subjected to a pressure change of

5.0 \times 10^{6} {Nm}^{- 2}

has its volume reduced by

3.0 \times 10^{- 7} m^{3}

. Find the coefficient of bulk modulus of the fluid.

MEDIUM

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>NUMERICALS>Q 21

1 m^{3}

of water is taken from the surface of a lake to a depth of

200 m

inside the lake. What will be the change in its volume if the bulk modulus of elasticity of water is

22000

atmospheres? (Density of water

= 1 \times 10^{3} kg m^{- 3}

, atmosphere pressure

= 10^{5} N m^{- 2}

and

g = 10 {ms}^{- 2}

.)

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>NUMERICALS>Q 22

A wire of length

1.0 m

bas area of cross-section

0.1 {cm}^{2}

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

2.5 \times 10^{11} {Nm}^{- 2}

and coefficient of linear thermal expansion is

2 \times 10^{- 5} ° C^{- 1}

. The wire is clamped between two rigid supports and its temperatures is decreased by

10 ° C

. Calculate the tension developed in it.

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>NUMERICALS>Q 23

The area of cross-section of metal rod is

1 {cm}^{2}

. It is clamped tightly at its two ends at

0 ° C

. The rod is heated to

100 ° C

. Calculate the tension produced at its two ends. Coefficient of linear expansion of metal is

1.2 \times 10^{- 5} ° C^{- 1}

and Young's modulus is

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

.

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>FOR DIFFERENT COMPETITIVE EXAMINATIONS>Q 1

The Young's modulus of a perfectly rigid material is:

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>FOR DIFFERENT COMPETITIVE EXAMINATIONS>Q 2

The Young's modulus for a perfectly plastic material is:

EASY

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>FOR DIFFERENT COMPETITIVE EXAMINATIONS>Q 3

In an experiment of determining Young's modulus of the material of a wire, the length as well the radius of the wire is doubled. The Young's modulus will:

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 18 - Elasticity>FOR DIFFERENT COMPETITIVE EXAMINATIONS>Q 4

A wire of length and cross-section $A$ hung from a rigid support is loaded by a mass $M$ . The elongation produced is: