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The length of an iron wire is L and area of cross-section is A. The increase in length is l on applying the force F on its two ends. Which of the statement is correct ?

(A)

Increase in length is inversely proportional to A

(B)

Increase in length is proportional to Young's modulus

(C)

Increase in length is inversely proportional to its length L

(D)

Increase in length is proportional to area of cross-section A

Question-2

A 5 m long steel wire is suspended from the ceiling of a room. A sphere of mass 25 kg and 10 cm radius is attached to another end of the wire. The height of the ceiling is 5.21 m. When the sphere is made to oscillate as a pendulum, then its lowest point just touches the floor. The velocity of the sphere at the lowest point will be :

(Given : Y = 2 x 10^{11}N/m^{2}, radius of wire = 0.05 cm)

(A)

3.71 m/s

(B)

3.71 cm/s

(C)

37.1 cm/s

(D)

37.1 m/s

Question-3

A uniform elastic plank moves due to a constant force F placed over a smooth surface. The area of end face is S and Young's modulus of the material is E. What is the average strain produced in the direction of the force?

(A)

^{F}/_{4SE}

(B)

Zero

(C)

^{F}/_{SE}

(D)

^{F}/_{2SE}

Question-4

For the same cross-sectional area and for a given load, teh ratio of depressions for the beam of a square cross-section and circular cross-section is :

(A)

3 : π

(B)

π : 3

(C)

1 : 1

(D)

1 : π

Question-5

A steel wire of uniform cross-section of 2 mm^{2} is heated upto 50^{o}C and clamped rigidly at two ends. If the temperature of wire falls to 30^{o}C then change in tension in the wire will be :

(Given : Coefficient of linear expansion of steel is 1.1 x 10^{-5°}C and Young's modulus of elasticity of steel is 2 x 10^{11}N/m^{2})

(A) 22N

(B)44 N

(C)88 N

(D)132 N

Question-6

The magnitude of the force developed by raising the temperature from 0^{o}C to 100^{o}C of the iron bar 1.00 m long and 1 cm^{2} cross-section when it is held so that it is not permitted to expand or bend is :

(Given : α = 10^{-5} /^{o}C and Y = 10^{11} N/m^{2})

(A)

10^{3 }N

(B)

10^{4 }N

(C)

10^{5 }N

(D)

10^{9 }N

Question-7

The volume of a solid rubber ball when it is carried from the surface to the bottom of a 200 m deep lake decreases by 0.1%. The value for bulk modulus of elasticity for rubber will be :

(A)

2 x 10^{9} pascal

(B)

2 x 10^{6} pascal

(C)

2 x 10^{4} pascal

(D)

2 x 10^{7} pascal

Question-8

The Young's modulus of a wire is Y. If the energy per unit volume is E, then the strain will be :

(A)

EY

(B)

E/Y

(C)

(D)

Question-9

An aluminium rod of Young's modulus 7.0 x 10^{9} N/m^{2} has a breaking strain of 0.2%. The minimum cross-sectional area of the rod in m^{2} in order to support a load of 10^{4} newton is :

(A)

1.0 x 10^{-2}

(B)

1.0 x 10^{-3}

(C)

1.4 x 10^{-2}

(D)

7.1 x 10^{-4}

Question-10

A bridge can bear 4 x 10^{4} kg weight. If the breaking stress is 47 x 10^{3} N/m^{3} and factor of safety is 5 then the area of cross section of the rod will be :^{ }

(A)

4.34 m^{2}

(B)

43.4 m^{2}

(C)

0.434 m^{2}

(D)

0.04 m^{2}

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