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 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 :
B
A
Both (a) and (b)
None of these
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
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
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
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 :
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
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?
F/4SE
Zero
F/SE
F/2SE
