Two rods of different materials having coefficients of linear expansion α1 and α2 , Young's modulii Y1 and Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α1 : α2 =2 : 3, the thermal stresses developed in the two rods are equal provided Y1 : Y2 is equal to :
2 : 3
1 : 1
3 : 2
4 : 9
For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is :
3 : π
π : 3
1 : π
The Young's modulus of a wire is Y. If the energy per unit volume is E, then the strain will be :
EY
E/Y
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 :
1/4 ρgL2/Y
1/2 ρgL2/Y
ρ gL2/Y
ρ gL/Y
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 1011N/m2, radius of wire = 0.05 cm)
3.71 m/s
3.71 cm/s
37.1 cm/s
37.1 m/s
The magnitude of the force developed by raising the temperature from 0oC to 100oC of the iron bar 1.00 m long and 1 cm2 cross-section when it is held so that it is not permitted to expand or bend is :
(Given : α = 10-5 /oC and Y = 1011 N/m2)
103 N
104 N
105 N
109 N
The bulk modulus of rubber is 9 x 108 N/m2. To what depth below the surface of sea should the rubber ball taken as to decrease its volume by 0.1%?
1 m
10 m
100 m
1 km
The upper end of a wire, 1 m long and 4 mm radius, is clamped. The lower end is twisted by an angle of 30o. The angle of shear at the surface is :
12o
1.2o
0.12o
0.012o
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 :
2 x 109 pascal
2 x 106 pascal
2 x 104 pascal
2 x 107 pascal
A steel wire of uniform cross-section of 2 mm2 is heated upto 50oC and clamped rigidly at two ends. If the temperature of wire falls to 30oC 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 1011N/m2)
22 N
44 N
88 N
132 N