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

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 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 $2.2 \times 10^{9} Nm$

Important Questions on Elasticity

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

= 1.36 \times 10^{- 2}

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

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 4

A wire of length

200 cm

and diameter

1.22 mm

is stretched between two rigid supports. When a load is suspended from the middle point of the wire, the point sags through

2 cm

. What is the value of the load?

Y

for the material of the wire

= 12.3 \times 10^{11}

dyne

{cm}^{- 2}

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 5

Show that if a wire of length

L

and cross-sectional area

A

is subjected to a given stress

S

within elastic limit, its potential energy per unit volume increases by

\frac{S^{2}}{2 Y}

. [

Y =

Young's modulus].

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 6

A wire of length

1

Metre when stretched by a load of

10 kg

Increases in length by

0.1 cm

. The cross-section of the wire is

0.1 {cm}^{2}

. Calculate Young's modulus of the material. If the Poisson's be

\frac{1}{3}

, calculate the change in volume of the wire.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 12 - Elasticity>EXERCISE>Q 7

A wire loaded by weights of density

9 {gcm}^{- 3}

is stretched to a length of

98 cm

. On immersing the weights in water, the length shortens by

2.5 mm

. Find the original length of the wire.

The average depth of Indian Ocean is about 3000 m. Calculate the fractional compression, ΔVV of water at the bottom of the ocean. Given that the bulk modulus of water is 2.2×109Nm

Important Questions on Elasticity

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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 $2.2 \times 10^{9} Nm$