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
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
The length of an iron wire is L and area of cross-section is A. The increase in length is l on applying the force F on its two ends. Which of the statement is correct ?
Increase in length is inversely proportional to A
Increase in length is proportional to Young's modulus
Increase in length is inversely proportional to its length L
Increase in length is proportional to area of cross-section A
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
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
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
A metal block is experiencing an atmospheric pressure of 105 N/m2. When the same block is placed in a vaccum chamber, the fractional change in its volume : (the bulk modulus of metal is 1.25 x 1011 N/m2)
8 x 10-7
1 x 10-7
4 x 10-7
2 x 10-7
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 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
