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
One end of a uniform wire of length L and weight W is attached rigidly to a point in roof and a weight W1 is suspended from its lower end. If S is the area of corss-section of the wire, the stress in the wire at a height of 3L/4 from its lower end is :
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 wire of density 9 gm/cm3 is stretched and clamped between two clamps distant 100 cm apart by a force which produces an elongation of 0.05 cm in it. If Y = 9 x 1011 dyne/cm2 then the minimum frequency of transverse vibrations will be :
15.15 per sec
25.25 per sec
35.35 per sec
53.53 per sec
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 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 :
8%
0.8%
0.08%
0.008%
In the given figure, if the dimensions of the wires are the same and materials are different, Young's modulus is more for :
Both (a) and (b)
None of these
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
A bridge can bear 4 x 104 kg weight. If the breaking stress is 47 x 103 N/m3 and factor of safety is 5 then the area of cross section of the rod will be :
4.34 m2
43.4 m2
0.434 m2
0.04 m2