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The upper end of a wire, 1 m long and 4 mm radius, is clamped. The lower end is twisted by an angle of 30^{o}. The angle of shear at the surface is :

(A)

12^{o}

(B)

1.2^{o}

(C)

0.12^{o}

(D)

0.012^{o}

Question-2

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-3

The bulk modulus of rubber is 9 x 10^{8} N/m^{2}. To what depth below the surface of sea should the rubber ball taken as to decrease its volume by 0.1%?

(A)

1 m

(B)

10 m

(C)

100 m

(D)

1 km

Question-4

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-5

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-6

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}

Question-7

A metal block is experencing an atmospheric pressure of 10^{5} N/m^{2}. When the same block is placed in a vaccum chamber, the fractional change in its volume : (the bulk modulus of metal is 1.25 x 10^{11} N/m^{2})

(A)

8 x 10^{-7}

(B)

1 x 10^{-7}

(C)

4 x 10^{-7}

(D)

2 x 10^{-7}

Question-8

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-9

A thick rope of density 'ρ' and length 'L' is hung from a rigid support. The Young's modulus of the material of rope is 'Y'. The increase in length of the rope due to its own weight is :

(A)

1/4 ρgL^{2}/Y

(B)

1/2 ρgL^{2}/Y

(C)

ρ gL^{2}/Y

(D)

ρ gL/Y

Question-10

The Poisson's ratio for a material is 0.1. If the longitudinal strain of a rod of this material is 1 x 10^{-3}, then the percentage change in the volume of rod will be :

(A)

8%

(B)

0.8%

(C)

0.08%

(D)

0.008%

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