The average depth of Indian Ocean is about 3000 m . Calculate the fractional compression, Δ V V of water at the bottom of the ocean. Given that the bulk modulus of water is 2 . 2 × 10 9 Nm

We know that, The water pressure formula. P = P o ρgh Where, P ∘ is the atmospheric pressure, g is acceleration due to gravity, h is the height from the Earth surface and ρ is density of water. It is given that, P o = 10 5 Nm - 2 , g = 10 ms - 2 , h = 3000 m and ρ = 10 3 Kgm - 3 Now, P = 10 5 + 10 3 × 10 × 3000 = 3 . 01 × 10 7 Nm - 2 Now we have to use the formula, B = P / - ∆ V V Here, B is bulk modulus and - ∆ V V is the fractional compression So, - ∆ V V = P B Now, put P = 3 . 01 × 10 7 Nm - 2 and B = 2 . 2 × 10 9 Nm - 2 Therefore, Fractional compression = 3 . 01 × 10 7 2 . 2 × 10 9 = 1 . 36 × 10 - 2

Two masses of 1 kg and 2 kg are connected by a metallic wire passing over a smooth pulley in Fig. The breaking stress of the metal = 2 × 10 9 Nm - 2 . What should be the minimum radius of the wire used if it does not snap ? g = 10 m / s 2 .

The tension in the wire, T = 2 m 1 m 2 m 1 + m 2 g ⇒ T = 2 × 1 × 2 1 + 2 × 10 ⇒ T = 40 3 N We know that, Breaking force = Breaking stress × Area of cross - section It is given that, Tension in the wire = 2 × 10 9 Nm - 2 ⇒ 40 3 = 2 × 10 9 × π r 2 r = 40 3 × 2 × 10 9 × 3 . 14 r = 4 . 6 × 10 - 3 cm Thus, the minimum radius of the wire is r = 4 . 6 × 10 - 3 cm

HARD

11th West Bengal Board

IMPORTANT

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The Poisson's ratio and Young's modulus of a light rod vertically suspended from one end, having length $300 cm$ and radius $3 cm$ are respectively $0.3$ and $2 \times 10^{12}$ dyne ${cm}^{- 2}$ . A load of $1200 kg$ is placed at the other end of the rod, Find the lateral strain of the rod.

Important Questions on Elasticity

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 12

A wire,

1 m

long when stretched by a load of

10 kg

extends

1 cm

in length. If the cross-section of the wire is

0.1 {cm}^{2}

and Poisson's ratio for the material of the wire is

1 / 3

, find the bulk modulus of the material of the wire.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 13

A steel rod

25 cm

long has a cross-sectional area of

0.8 {cm}^{2}

What force would be required to stretch this rod by the same amount as the expansion produced by heating it through

10 ° C

? Co-eff

^{n}

of linear expansion of steel

= 10^{- 5} / {}^{\circ}C

Y

for steel

= 20 \times 10^{11}

dyne

{cm}^{- 2}

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 14

A wire

A B

of radius

0.3 mm

and length

300 cm

is attached to a fixed support and hangs vertically. The wire carries a load

4 kg

attached to its mid-point

C

and also another load of

4 kg

at its lower end

B

.. If

Y

for the material of the wire be

2 \times 10^{12}

dyne

{cm}^{- 2}

, find the depression of the end

B

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 15

The average depth of Indian Ocean is about

3000 m

. Calculate the fractional compression,

\frac{Δ V}{V}

of water at the bottom of the ocean. Given that the bulk modulus of water is

2.2 \times 10^{9} Nm

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 16

A wire of circular cross-section is stretched by a longitudinai force and its change in length is found be

0.01 %

. If the Poisson's ratio for the material is

0.2

, what is the percentage of change in volume?

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 1

A sphere of weight

10 N

is fastened to one end of a wire of cross-sectional area

3 {mm}^{2}

and is rotated in a vertical circle of radius

20 cm

. The speed of the sphere at the bottom of the circle is

2 {ms}^{- 1}

. Find the elongation of the wire when the sphere is at the bottom of the circle.

Y

for the wire

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

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 2

Three weightless springs of equal length

l

, have force constant

K_{1}, K_{2}

and

K_{3}

respectively and are connected as shown in figure. Show that the force constant

K

of the spring system is given by,

K = K_{1} + K_{2} + K_{3}

Question Image

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 3

Two masses of

1 kg

and

2 kg

are connected by a metallic wire passing over a smooth pulley in Fig. The breaking stress of the metal

= 2 \times 10^{9} {Nm}^{- 2}

. What should be the minimum radius of the wire used if it does not snap ?

g = 10 m / s^{2}

Question Image

The Poisson's ratio and Young's modulus of a light rod vertically suspended from one end, having length 300 cm and radius 3 cm are respectively 0.3 and 2×1012 dyne cm-2. A load of 1200 kg is placed at the other end of the rod, Find the lateral strain of the rod.

Important Questions on Elasticity

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The Poisson's ratio and Young's modulus of a light rod vertically suspended from one end, having length $300 cm$ and radius $3 cm$ are respectively $0.3$ and $2 \times 10^{12}$ dyne ${cm}^{- 2}$ . A load of $1200 kg$ is placed at the other end of the rod, Find the lateral strain of the rod.