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 breaking stress of a wire depends upon:
1. | material of the wire. |
2. | length of the wire. |
3. | radius of the wire. |
4. | shape of the cross-section. |
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.
Copper of fixed volume V is drawn into a wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is Δl. Which of the following graphs is a straight line?
(1) Δl versues 1/l
(2) Δl versus l2
(3) Δl versus 1/l2
(4) Δl versus l
The Young's modulus of a wire of length L and radius r is If the length and radius are reduced to L/2 and r/2, then its Young's modulus will be -
(1) Y
(2) 4Y
(3) 8Y
(4)
When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, then the increase in length will be -
(1) 0.5 cm
(2) 2 cm
(3) 4 cm
(4) 8 cm
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
A force \(F\) is needed to break a copper wire having radius \(R.\) The force needed to break a copper wire of radius \(2R\) will be:
1. | \(F/2\) | 2. | \(2F\) |
3. | \(4F\) | 4. | \(F/4\) |
If x longitudinal strain is produced in a wire of Young's modulus y, then energy stored in the material of the wire per unit volume is-
1.
2.
3.
4.
A and B are two wires of same material. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is
(1) Equal to that on A
(2) Four times that on A
(3) Two times that on A
(4) Half that on A
If the length of a wire is reduced to half, then it can hold the ......... load
(1) Half
(2) Same
(3) Double
(4) One fourth
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
The force constant of a wire does not depend on
(1) Nature of the material
(2) Radius of the wire
(3) Length of the wire
(4) None of the above
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)
Which one of the following quantities does not have the unit of force per unit area?
1. Stress
2. Strain
3. Young's modulus of elasticity
4. Pressure
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
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
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 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
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)
When a spiral spring is stretched by suspending a load on it, the strain produced is called:
1. | Shearing |
2. | Longitudinal |
3. | Volume |
4. | shearing and longitudinal |
If the Young's modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be
(a) Zero (b) Infinity
(c) (d)
One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(S\) is the area of cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W_1}{S}\)
2. \(\frac{W_1+\left(\frac{W}{4}\right)}{S}\)
3. \(\frac{W_1+\left(\frac{3W}{4}\right)}{S}\)
4. \(\frac{W_1+W}{S}\)
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
If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be
(1) V/25
(2) 5V
(3) V/5
(4) 25V
Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be
(1) 1 : 2
(2) 1 : 4
(3) 2 : 1
(4) 1 : 1
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)
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.
The length of elastic string, obeying Hooke's law is metres when the tension is 4N, and metres when the tension is 5N. The length in metres when the tension is 0 N will be:
1.
2.
3.
4.
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
(1) Length = 50 cm, diameter = 0.5 mm
(2) Length = 100 cm, diameter = 1 mm
(3) Length = 200 cm, diameter = 2 mm
(4) Length = 300 cm, diameter = 3 mm
Copper of fixed volume 'V' is drawn into wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is . Which of the following graph is a straight line?
(1) versus l/l
(2) versus
(3) versus
(4) versus l
The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of
(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 4 : 1
The bulk modulus of a spherical object is B. If it is subjected to uniform pressure P, the fractional decrease in radius is
(1)
(2)
(3)
(4)
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by on applying a force F, how much force is needed to stretch the second wire by the same amount?
(1) 4F
(2) 6F
(3) 9F
(4) F