Elasticity worksheet for Class 11 Physics

The possible value of Poisson’s ratio ($\sigma$) for any material can be:

1. a Between 0 and 0.5
2. b Between 0.5 and 1.5
3. c Between −1 and −2
4. d Between 0.5 and −1

Shearing strain is equivalent to:

1. a An extension strain
2. b A compressive strain
3. c The sum of mutually parallel expansion and contraction strains
4. d The sum of mutually perpendicular expansion and contraction strains

When a wire is twisted, the strain produced in it is:

1. a Normal strain
2. b Longitudinal strain
3. c Lateral strain
4. d Shearing strain

If two identical balls, one made of ivory and the other made of clay, are dropped from the same height onto the floor, then:

1. a The ivory ball will bounce to a higher height
2. b The clay ball will bounce to a higher height
3. c Both balls will bounce to the same height
4. d The ivory ball will not bounce at all

Which of the following is the most elastic material?

1. a Glass
2. b Quartz
3. c Steel
4. d Rubber

The following four wires are made of the same material. On applying the same tension, which one will have the maximum increase in length?

1. a Length 50 cm, diameter 0.5 mm
2. b Length 100 cm, diameter 1 mm
3. c Length 200 cm, diameter 2 mm
4. d Length 300 cm, diameter 3 mm

A wire of length $L$ and cross-sectional area $A$ is made of a material whose Young’s modulus is $Y$. If an extension $x$ is produced in its length, the work done is:

1. a $\dfrac{Yx^2}{2}$
2. b $\dfrac{YAx^2}{2L}$
3. c $YAx^2$
4. d $\dfrac{Yx^2}{L^2}$

Copper wires are more easily drawn out than iron wires because:

1. a Copper is a good conductor of heat
2. b The resistance of copper is less
3. c The modulus of rigidity of copper is high
4. d The Young’s modulus of copper is high

In a metallic wire, if the stress is $T$ and the Young’s modulus is $Y$, then the energy stored per unit volume is:

1. a $\dfrac{TY^2}{2}$
2. b $\dfrac{TY}{2}$
3. c $TY$
4. d $\dfrac{T^2}{2Y}$

Elasticity is a property of matter that is:

1. a Molecular in nature
2. b Electromagnetic in nature
3. c Nuclear in nature
4. d Gravitational in nature

The relation between $Y$, $\eta$ and $K$ is:

1. a $\dfrac{1}{9Y} = \dfrac{1}{3\eta} + \dfrac{1}{K}$
2. b $\dfrac{1}{K} = \dfrac{1}{3Y} + \dfrac{1}{9\eta}$
3. c $\dfrac{1}{\eta} = \dfrac{1}{3Y} + \dfrac{1}{9K}$
4. d $\dfrac{1}{Y} = \dfrac{1}{3\eta} + \dfrac{1}{9K}$

The relation between $Y$, $\eta$ and $\sigma$ is:

1. a $\dfrac{1}{\eta} = 2(1 + 2\sigma)$
2. b $Y = 2\eta(1 + \sigma)$
3. c $\eta = 2Y(1 + 2\sigma)$
4. d $Y = 3\eta(1 - 2\sigma)$

If the radius of a wire and the force applied to it are both doubled, then the increase in its length will become:

1. a Four times
2. b Two times
3. c Unchanged
4. d Half

The Young’s modulus of elasticity of a wire material is $2 \times 10^{11}$ N/m². If the strain produced in it is 0.15, then the applied stress (in N/m²) will be:

1. a $3 \times 10^{10}$
2. b $3 \times 10^{11}$
3. c $2 \times 10^{11}$
4. d $2 \times 10^{10}$

The dimensions of strain are the same as those of which of the following quantities?

1. a Stress
2. b Modulus of elasticity
3. c Angle
4. d Pressure

When a weight is suspended from one end of a wire, the wire gets stretched. The potential energy per unit volume of the wire in terms of longitudinal strain $\sigma$ and Young’s modulus $Y$ will be:

1. a $\dfrac{Y\sigma^2}{2}$
2. b $\dfrac{Y\sigma}{2}$
3. c $\dfrac{2Y\sigma^2}{2}$
4. d $\dfrac{Y^2\sigma}{2}$

The upper end of a wire of radius 4 mm and length 100 cm is clamped, and the other end is twisted by $30^\circ$. The shearing angle will be:

1. a $12^\circ$
2. b $0.12^\circ$
3. c $1.2^\circ$
4. d $0.012^\circ$

The Young’s modulus of a given substance is 2.4 times its modulus of rigidity. Its Poisson’s ratio will be:

1. a 2.4
2. b 1.2
3. c 0.4
4. d 0.2

On applying a load to a wire, its length increases by 3 mm. The extension in another wire of the same material and same length, but whose radius is half, under the same load will be:

1. a 12 mm
2. b 0.75 mm
3. c 6 mm
4. d 15 mm

How much force is required to stretch a steel wire of cross-sectional area 1 cm² to 1.1 times its length?

1. a $2 \times 10^{6}$ N
2. b $2 \times 10^{3}$ N
3. c $2 \times 10^{-6}$ N
4. d $2 \times 10^{-7}$ N

A wire of length $L$ and cross-sectional area $A$ has a Young’s modulus of elasticity $Y$. If the length of the wire is doubled and the cross-sectional area is halved, then the Young’s modulus of elasticity of the wire will become:

1. a $4Y$
2. b $Y$
3. c $2Y$
4. d $Y/2$

The edge of a solid copper cube is 10 cm. When a hydraulic pressure of $7.20 \times 10^{6}$ Pa is applied to it, its volume contracts by 0.06 cm³. Find the bulk modulus of copper.

Two wires A and B of different metals, having the same radius and equal length, are joined together to make a long wire. By fixing one end of it and applying a force on the other end, the elongation in the length of this composite wire is 4 cm. If $Y_B = 3Y_A$, find the change in length of wire B. ($Y$ = Young’s modulus of elasticity)

Find the work done per unit volume to increase the length of a wire by 1%, having Young’s modulus $Y$ and a cross-sectional area of 1 mm². ($Y = 9 \times 10^{11}$ N/m²)

What is the density of water at a depth where the pressure is 80.0 atm, given that its density at the surface is $1.03 \times 10^{3}$ kg m$^{-3}$?