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

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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?

MEDIUM

11th West Bengal Board

IMPORTANT

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

Two masses of

= 1.36 \times 10^{- 2}

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

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 11

A $0.5 kg$ block slides from a point $A$ (see Fig) on a horizontal track with an initial speed of $3 m / s$ towards a weightless horizontal spring of length $1 m$ and force constant $2 N / m$ . The part $A B$ of the track is frictionless and the part $B C$ has the coefficient of static and kinetic friction as $0.22$ and $0.2$ respectively. If the distance $A B$ and $B D$ are $2 m$ and $2.14 m$ respectively, find the total distance through which the block moves before it completely stops. (Take $g = 10 m / s^{2}$ ).

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HARD

11th West Bengal Board

IMPORTANT

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

A uniform rod of length

L

and density

ρ

is being pulled along a smooth floor with a horizontal acceleration

a

. Find the magnitude of the stress at the transverse cross-section through the mid-point of the rod

HARD

11th West Bengal Board

IMPORTANT

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

A steel wire of cross-section

A

is stretched horizontally between two clamps located at a distance

l

from each other. A load

W

is suspended from the mid-point of the wire. What is the vertical distance through which the mid-point of the wire moves down ? Young's modulus of steel is

Y

MEDIUM

11th West Bengal Board

IMPORTANT

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

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied :

EASY

11th West Bengal Board

IMPORTANT

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

A spring of force constant

K

is cut into two equal parts. The force constant of each part is

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 $2.2 \times 10^{9} Nm$