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 :
3 : π
π : 3
1 : 1
1 : π
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 force of 200 N is applied at one end of a wire of length 2 m and having area of cross-section 10-2 cm2. The other end of the wire is rigidly fixed. It coefficient of linear expansion of the wire α = 8 x 10-6/oC and Young's modulus Y = 2.2 x 1011 N/m2 and its temperature is increased by 5oC, then the increase in the tension of the wire will be :
2.4 N
8.8 N
4.2 N
4.4 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%
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
3 : 2
4 : 9
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
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
An aluminium rod of Young's modulus 7.0 x 109 N/m2 has a breaking strain of 0.2%. The minimum cross-sectional area of the rod in m2 in order to support a load of 104 newton is :
1.0 x 10-2
1.0 x 10-3
1.4 x 10-2
7.1 x 10-4
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
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 :
