A gas undergoes a process in which its pressure P and volume V are related as . The bulk modulus for the gas in the process is:
[This question includes concepts from Kinetic Theory chapter]
1.
2.
3. nP
4.
The Young's modulus of a wire of length 'L' and radius 'r' is 'Y'. If length is reduced to L/2 and radius r/2, then Young's modulus will be
1. Y/2
2. Y
3. 2Y
4. 4Y
Three wires A, B, C made of the same material and radius have different lengths. The graphs in the figure show the elongation-load variation. The longest wire is
1. | A | 2. | B |
3. | C | 4. | All |
The elastic energy stored in a wire of Young's Modulus Y is -
1.
2.
3.
4.
The bulk modulus of a spherical object is B. If it is subjected to uniform pressure P, the fractional decrease in radius will be:
1.
2.
3.
4.
The area of cross-section of a wire of length \(1.1\) m is \(1\) mm2. It is loaded with mass of \(1\) kg. If Young's modulus of copper is \(1.1\times10^{11}\) N/m2, then the increase in length will be: (If )
1. | \(0.01\) mm | 2. | \(0.075\) mm |
3. | \(0.1\) mm | 4. | \(0.15\) mm |
In the CGS system, Young's modulus of a steel wire is 2×1012 dyne/cm2. To double the length of a wire of unit cross-section area, the force required is:
1. 4×106 dynes
2. 2×1012 dynes
3. 2×1012 newtons
4. 2×108 dynes
Two wires of copper having length in the ratio of 4: 1 and radii ratio of 1: 4 are stretched by the same force. The ratio of longitudinal strain in the two will be:
1. 1: 16
2. 16: 1
3. 1: 64
4. 64: 1
A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be
(a) l (b) 2l
(c) (d)
In steel, the Young's modulus and the strain at the breaking point are and 0.15 respectively. The stress at the breaking point for steel is therefore -
(1)
(2)
(3)
(4)
When a weight of 10 kg is suspended from a copper wire of length 3 metres and diameter 0.4 mm, its length increases by 2.4 cm. If the diameter of the wire is doubled, then the extension in its length will be
(a) 9.6 cm (b) 4.8 cm
(c) 1.2 cm (d) 0.6 cm
A fixed volume of iron is drawn into a wire of length L. The extension x produced in this wire by a constant force F is proportional to:
(1)
(2)
(3)
(4) L
On applying stress of \(20 \times 10^8~ \text{N/m}^2\), the length of a perfectly elastic wire is doubled. It's Young’s modulus will be:
1. | \(40 \times 10^8~ \text{N/m}^2\) | 2. | \(20 \times 10^8~ \text{N/m}^2\) |
3. | \(10 \times 10^8~ \text{N/m}^2\) | 4. | \(5 \times 10^8~ \text{N/m}^2\) |
The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is
(1) a - b
(2) 5b - 4a
(3) 2b -
(4) 4a - 3b
How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm ?
(Young’s modulus for brass = )
(a) Nearly 17 N (b) Nearly 34 N
(c) Nearly 51 N (d) Nearly 68 N
A 5 m long aluminium wire of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire of the same length under the same weight, the diameter of the copper wire should be, in mm:
(a) 1.75 (b) 1.5
(c) 2.5 (d) 5.0
A steel wire of 1 m long and cross section area is hang from rigid end. When mass of 1kg is hung from it then change in length will be: (given )
(1) 0.5 mm
(2) 0.25 mm
(3) 0.05 mm
(4) 5 mm
A force F is applied on the wire of radius r and length L and change in the length of wire is l. If the same force F is applied on the wire of the same material and radius 2r and length 2L, Then the change in length of the other wire is
(a) l (b) 2l
(c) (d) 4l
An iron rod of length 2m and cross section area of 50 X , is stretched by 0.5 mm, when a mass of 250 kg is hung from its lower end. Young's modulus of the iron rod is-
(1)
(2)
(3)
(4)
In which case, there is a maximum extension in the wire, if the same force is applied on each wire?
(1) L = 500 cm, d = 0.05 mm
(2) L = 200 cm, d = 0.02 mm
(3) L = 300 cm, d = 0.03 mm
(4) L = 400 cm, d = 0.01 mm
The extension of a wire by the application of load is 3 mm. The extension in a wire of the same material and length but half the radius by the same load is -
(1) 12 mm
(2) 0.75 mm
(3) 15 mm
(4) 6 mm
The isothermal elasticity of a gas is equal to
(1) Density
(2) Volume
(3) Pressure
(4) Specific heat
The adiabatic elasticity of a gas is equal to
1. γ × density
2. γ × volume
3. γ × pressure
4. γ × specific heat
The specific heat at constant pressure and at constant volume for an ideal gas are and and its adiabatic and isothermal elasticities are and respectively. The ratio of to is
(1)
(2)
(3)
(4)
The compressibility of water is per unit atmospheric pressure. The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere will be -
(a) 0.4 cc (b)
(c) 0.025 cc (d) 0.004 cc
If a rubber ball is taken at the depth of 200 m in a pool, its volume decreases by 0.1%. If the density of the water is and , then the volume elasticity in will be
(1)
(2)
(3)
(4)
When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces by 0.01%. The bulk modulus of the material of the rubber in is:
(1)
(2)
(3)
(4)
A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is
(1) 0.01
(2) 0.06
(3) 0.02
(4) 0.03
A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball
(1)
(2)
(3)
(4)
The Bulk modulus for an incompressible liquid is
(1) Zero
(2) Unity
(3) Infinity
(4) Between 0 to 1
The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is and the coefficient of volume expansion is -
(1)
(2)
(3)
(4)
The strain-stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that:
1. | Elasticity of wire P is maximum |
2. | Elasticity of wire Q is maximum |
3. | Tensile strength of R is maximum |
4. | None of the above is true |
The diagram shows a force-extension graph for a rubber band. Consider the following statements
I. It will be easier to compress this rubber than expand it
II. Rubber does not return to its original length after it is stretched
III. The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph?
(1) III only
(2) II and III
(3) I and III
(4) I only
The adjacent graph shows the extension of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is calculate the young’s modulus of the material of the wire
(a)
(b)
(c)
(d)
The graph shows the behaviour of a length of wire in the region for which the substance obeys Hook’s law. \(P\) and \(Q\) represents:
1. | \(P\) = applied force, \(Q\) = extension |
2. | \(P\) = extension, \(Q\) = applied force |
3. | \(P\) = extension, \(Q\) = stored elastic energy |
4. | \(P\) = stored elastic energy, \(Q\) = extension |
The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that
(1) A is brittle but B is ductile
(2) A is ductile and B is brittle
(3) Both A and B are ductile
(4) Both A and B are brittle
The work done in stretching an elastic wire per unit volume is:
1. | stress\(\times\)strain |
2. | \(\frac{1}{2}\) \(\times\) stress\(\times\)strain |
3. | \(2\times\) stress\(\times\)strain |
4. | stress/strain |
A \(5\) m long wire is fixed to the ceiling. A weight of \(10\) kg is hung at the lower end and is \(1\) m above the floor. The wire was elongated by \(1\) mm. The energy stored in the wire due to stretching is:
1. zero
2. \(0.05\) J
3. \(100\) J
4. \(500\) J
A wire is suspended by one end. At the other end a weight equivalent to 20 N force is applied. If the increase in length is 1.0 mm, the increase in energy of the wire will be
(1) 0.01 J
(2) 0.02 J
(3) 0.04 J (4) 1.00 J
The ratio of Young's modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be-
(1) 3 : 2
(2) 2 : 3
(3) 3 : 4
(4) 4 : 3
The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If and are the Young ‘s modulii of the materials, then
(1)
(2)
(3)
(4)
The Young's modulus of a wire is Y. If the energy per unit volume is E, then the strain will be:
1.
2.
3.
4.
When a force is applied on a wire of uniform cross-sectional area and length 4m, the increase in length is 1 mm. Energy stored in it will be
1. 6250 J 2. 0.177 J
3. 0.075 J 4. 0.150 J
A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y.\) It is stretched by an amount \(x.\) The work done is:
1.
2.
3.
4.
The work done per unit volume to stretch the length of a wire by 1% with a constant cross-sectional area will be:
1.
2.
3.
4.