A wire of length L and cross - sectional area A is made of a material of Young's modulus Y. If the wire is stretched by an amount x, the work done is ;
Y Ax2 / 2L
Y Ax2 / L
Y Ax / 2L
Y Ax2 L
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 wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is :
0.2 J
10 J
20 J
0.1 J
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
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
Which of the following has no dimensions?
Strain
Angular velocity
Momentum
Angular Momentum
A substance breaks down by a stress of 106 N / m 2. If the density of the material of the wire is 3 X 103 kg / m 3, then the length of the wire of the substance which will break under its own weight when suspended vertically will be :
66.6 m
60.0 m
33.3 mm
30.3 mm
The following for wires are made of the same material. Which of these will have the largest extension, when the same tension is applied ?
length = 50 cm, diameter = 0.5 mm
length = 100 cm, diameter = 1 mm
length = 200 cm, diameter = 2mm
length = 300 cm, diameter = 3 mm
There are two wires of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wire by applying same load will be :
2 : 1
1 : 2
4 : 1
A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching will be :
F / 2l
Fl
2 Fl
Fl / 2