Longitudinal Strain

Q.

A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44, 500 N force, producing only elastic deformation. Calculate the resulting strain? (Take modulus of elasticity of copper $140\times {10}^{9}m/se{c}^2$)

Q. A wire elongates by 1.0 mm when a load W is hanged from it. If this wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be

1. 
2. 
3. 
4. 

Q. The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied

1. Length 100 cm, diameter 1 mm
2. Length 200 cm, diameter 2 mm
3. Length 300 cm, diameter 3 mm
4. Length 50 cm, diameter 0.5 mm

Q. A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig. 9.15. The cross-sectional areas of wires A and B are 1.0 mm² and 2.0 mm², respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.

Q. A block of weight 10 N is fastened to one end of a wire of cross-sectional area 3 mm² and is rotated in a vertical circle of radius 20 cm. The speed of the block at the bottom of the circle is 2 m s^-1. Find the elongation of the wire when the block is at the bottom of the circle. Young modulus of the material of the wire = 2 x 10¹¹ N m^-2.

1. 

2. 

3. 2 cm

4. 2 cm

Q. When a load of 10N is hanged from a wire, the elongation produced is x mm. If the wire goes over a pulley and two weights 10N each are hung at the two ends, the elongation of the wire will be(in mm)

Q. A block of 10 g slides on smooth horizontal surface with 20 m/s towards a spring of spring constant100 N/m placed horizontally (as shown in figure). The maximum compression in spring is

Q. 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path

Q. Strain is a dimensionless quantity.

1. False
2. True

Q. The length of an elastic string is ametres when the longitudinal tension is 4 N and bmetres when the longitudinal tension is 5 N. The length of the string in metres when the longitudinal tension is 9 N is

1. 
2. 
3. 
4. 

Q.

The length of the wire is increased by 1 mm on the application of a given load. In a wire of the same material but of length and radius twice that of the first, on application of the same force, extension produced is

1. 4 mm

2. 0.25 mm

3. 2 mm

4. 0.5 mm

Q. : A square glass plate of length 10 cm and thickness O.4 cm, weighs 40 g in air. It is held verticallysuch that its lower edge rests on water surface. What is the apparent weight of glass plate now?(Given surface tension of water 0.073 N m1)

Q. Strain is a dimensionless quantity.

1. False
2. True

Q.

A 30kg hammer strikes a steel spike (nail) 2.30 cm in diameter while moving with speed 20.0 m/s. The hammer rebounds with speed 10.0 m/s after 0.110s. The average strain in the spike during the impact will be

($Y=2\times {10}^{11}N/m^2$)

1. 10^-2

2. 10^-3

3. 10^-4

4. 10^-5

Q. The Young’s modulus of steel is twice as 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. $2:1$
2. $4:1$
3. $1:2$
4. $1:1$

Q. Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that ofbrass wire is 1.0 m. Compute the elongations of the steel and the brass wires.

Q.

When a 13.2 kg mass is placed on top of a vertical spring, the spring compresses by 5.93 cm. Find the force constant of the spring.

1. 3085 N/m

2. 3181 N/m

3. 2281 N/m

4. 2175 N/m

Q. monkey was climbing a rope whose accleration is 2m/s-2 and mass is 40 kg find the tension in the rope

Q. 45.A block of mass m is to be raised by a light rope from rest to rest through a height 60 m, the maximum tension of which the rope can safely bear is 4mg. The least time in which the ascent can be made is

Q. A wire of cross-section area $2{\text{mm}}^2$ is stretched by $0.1\text{mm}$ by a certain force. How far (length) will the wire of same material and length but area $8{\text{mm}}^2$ stretch under the action of same force?

1. $0.25\text{mm}$
2. $0.005\text{mm}$
3. $0.025\text{mm}$
4. $0.05\text{mm}$

Q. Two blocks of masses $m_1$ and $m_2$ are joined by a wire of Young’s modulus Y via a massless pulley. The area of cross-section of the wire is S and its length is L. When the system is released, increase in length of the wire is

1. 
2. 
3. 
4. 

Q. Three blocks, each of same mass m, are connected with wires $W_1$ and $W_2$ of same cross- sectional area a and Young's modulus Y. Neglecting friction the strain developed in wire $W_2$ is

1. 
2. 
3. 
4. 

Q. Two persons hold a rope of negligible weight tightly at its ends so that it is horizontal. A 15 kg weight isattached to the rope at the mid point which is nowno longer remains horizontal. The minimum tension required to completely straighten the top is(1) 15/2 kg(2) Infinitely large(3)15 kg(4) 5 kg

Q. Four identical hollow cylindrical columns of mild steel support a big structure of mass 50, 000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

Q.

Two wires of equal cross section but one made of steel and the other of copper are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. Find the ratio of the lengths of the two wires. Young modulus of steel = 2.0 x 10¹¹ N m^-2 and that of copper = 1.1 x 10¹¹ N m^-2.

1. 

2. 

3. 

4. 

Q. A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is

1. Smallest at the top and gradually increases down the rod

2. Largest at the top and gradually decreases down the rod

3. Maximum in the middle

4. Uniform everywhere

Q. A fan of weight Wf is suspended from the ceiling of a hall through a chain of weight Wc. How much force exerted by ceiling to the chain?

Q.

The graph shows the behaviour of a length of wire in the region for which the substance obeys Hook's law. P and Q represent

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

Q. A wire elongates by 1.0 mm when a load W is hanged from it. If this wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be

1. $0.5m$
2. $1.0m$
3. $2.0mm$
4. $4.0mm$

Q. Three blocks, each of same mass m, are connected with wires $W_1$ and $W_2$ of same cross- sectional area a and Young's modulus Y. Neglecting friction the strain developed in wire $W_2$ is

1. $\frac{2}{3}\frac{mg}{aY}$
2. $\frac{3}{2}\frac{mg}{aY}$
3. $\frac{1}{3}\frac{mg}{aY}$
4. $\frac{3mg}{aY}$