Longitudinal Strain

Q.

A wire elongates by $\mathrm{l}\mathrm{mm}$ when a load $\mathrm{W}$ is hanged from it. If the wire goes over a pulley and two weighs $\mathrm{W}$ each is hung at the two ends, the elongation of the wire will be (in $\mathrm{mm}$)

1. $\frac{\mathrm{l}}{2}$

2. $\mathrm{l}$

3. $2I$

4. Zero

Q. A wire is stretched to double its length. The strain is

1. 2
2. 1
3. 0
4. 0.5

Q.

Two wires of same material and radius have their lengths in ratio 1:2. If these wires are stretched by the same force, the strain produced in the two wires will be in the ratio

1. 2:1
2. 1:1
3. 1:2
4. 1:4

Q. The length of a wire increases by 1% by a load of 2 kg-wt. The linear strain produced in the wire will be

1. 0.001
2. 0.01
3. 0.02
4. 0.002

Q. A wire is stretched by 0.01 m by a certain force F. Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be

1. 0.005 m
2. 0.01 m
3. 0.02 m
4. 0.002 m

Q.

A wire extends by 1 mm when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross section. The elongation of the wire in mm will be

1. 1
2. 4
3. 2
4. 8

Q. Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has length 2l and diameter 2r. If the two wires are stretched by the same force, the elongation in A divided by elongation in B is

1. 1/8

2. 1/4

3. 4

4. 8

Q. A wire extends by 1 mm when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be

1. 8
2. 4
3. 2
4. 1

Q. A 6-kg weight is fastened to the end of a steel wire of un-stretched length 60 cm. It is whirled in a vertical circle and has an angular velocity of 2 revolutions per second at the bottom of the circle. The area of cross-section of the wire is $0.05c{m}^2$. Calculate the elongation of the wire when the weight is at the lowest point of the path. Young's modulus of steel = $2\times {10}^{11}$ Pa.

1. 4.97 m

2. 3.77 m

3. 2.34m

4. 2.34m

Q. Each of the three blocks P, Q and R shown in figure have a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm² and Young modulus 2 x 10¹¹ N m^-2. Neglect friction. Find the longitudinal strain developed in each of the wires. Take g = 10 m s^-2.

1. 
2. 
3. 
4. 

Q. A nucleus breaks into two parts whose velocities are in the ratio 2 : 1. The ratio of their radius is

1. $1:2^{\frac{2}{3}}$
2. $1:2^{\frac{1}{3}}$
3. $2^{\frac{2}{3}}:1$
4. $2^{\frac{1}{2}}:1$

Q.

Two identical wires of rubber and iron are stretched by the same weight, then the number of atoms in the iron wire will be

1. equal to that of rubber
2. less than that of the rubber
3. more than that of rubber
4. none of the above

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 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. 4a - 3b
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. A uniform heavy rod of weight W, cross-sectional area A and length L is hanging from a fixed support. Young modulus of the material of the rod is Y. Neglect the lateral contraction. Find the elongation of the rod.

1. 

2. 

3. 

4. 

Q. Consider the following two statements A and B and identify the correct answer.
A) The product of bulk modulus of elasticity and compressibility is one.
B) Tangential stress applied on the body only produes change in shape but not in size.

1. Both A & B are true
2. A is false but B is true
3. A is true but B is false
4. Both A & B are false

Q.

Two wires A and B of the same material have their lengths in the ratio of 1:2 and their diameters in the ratio of 2:1. If they are stretched with the same force, the ratio of the increase in the length of A to that of B will be

1. 1:2

2. 4:1

3. 1:8

4. 1:4