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Two wires of the same material and length but diameters in the ratio 1 : 2 are stretched by the sameforce.
The potential energy per unit volume for the two wires when stretched will be in the ratio
1 : 1
4 : 1
2 : 1
16 : 1
A helical spring extends 40 mm when stretched by a force of 10 N, and for tensions up to this value the extension is proportional to the stretchingforce.
Two such springs are joined end to-end and the double-length spring is stretched 40 mm beyond its naturallength.
The total strain energy, in J, stored in the double spring is
0.10
0.20
0.05
0.40
A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8radius.
The shear strain developed will be
0.002
0.016
0.008
0.004
The length of an elastic string is a metre when the tension is 4 N, and b metre when the tension is 5 N. The length in metre when the tension is 9 N is
4a - 5b
b - a
a + b
5b - 4a
A cube of aluminium of sides 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottomface.
The shearing strain would be
0.1
0.005
0.02
0.002
A force F is required to break a wire or length l and radius r. What force is required to break a wire, of the same material, having twice the length and six times the radius
3 F
36 F
9 F
F
A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lowerend.
If its radius is r, its length L and Young s modulus for the material of the wire is E, the extension is
(1) directly proportional to E
(2) inversely proportional to r.
(3) directly proportional to L
if 1, 2, 3 are correct
if 2, 3 are correct
if 1, 2 are correct
if 3 only is correct
Two identical wires are suspended from the same rigid support but one is of copper and the other is ofiron.
Young s modulus of iron is thrice that ofcopper.
The weights to be added on copper and iron wires so that the ends are on the same level must be in the ratio of
3 : 1
2 : 1
4 : 1
1 : 3
If the work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by 1 mm is
4 J
8 J
1 / J
16 J
Two wires of the same material and length are stretched by the sameforce.
Their masses are in the ratio 3 : 2. Their elongations are in the ratio
3 : 2
9 : 4
2 : 3
4 : 9
A wire extends by 1 mm when a force isapplied.
Double the force is applied to another wire of same material and length but half the radius of cross-section.
The elongation of the wire in mm will be
4
8
2
1
A wire of length L and radius r is clamped rigidly at oneend.
When the other end of the wire is pulled by a force F, its length increases by l
. Another wire of the same material of length 4 L and radius 4r, is pulled by a force 4F. The increase in length will be
L / 2
4l
L
2l
A piece of copper wire has twice the radius of a piece of steelwire.
The Young s modulus for steel is twice that for thecopper.
One end of the copper wire is joined to one end of the steel wire so that both can be subjected to the same longitudinalforce.
By what fraction of its length of the copper has increased by 1%
1%
3%
2.5%
2%
The increase in length on stretching a wire is 0.05%. If its Poisson s ratio is 0.4, the diameter is reduced by
0.04%
0.03%
0.02%
0.01%
Three wires P,Q and R of the same material and length have radii 0.1 cm, 0.2 cm and 0.3 cmrespectively.
Which wire has the highest value of Young s modulus of elasticity
Q
R
P
All have the same value
When a 4 kg mass is hung vertically on a light spring that obeys Hooke s law, the spring stretches by 2 cm. The work required to be done by an external agent in stretching this spring by 5 cm will be
0.495 J
2.45 J
0.245 J
4.9 J
When a weight of 5 kg is suspended from a copper wire of length 30 m anddiameter.
0.5, the length of the wire increases by 2.4 cm. If the diameter is doubled, the extension produced is
0.3 cm
0.6 cm
0.15 cm
1.2 cm
Two wires of the same material and same are stretched by the sameforce.
Their lengths are in the ratio 2 : 3. Their elongations are in the ratio
4 : 9
3 : 2
9 : 4
2 : 3
A 100 N force stretches the length of a hanging wire by 0.5 mm. The force required to stretch a wire, of the same material and length but having four times the diameter, by 0.5 mm is
1200 N
400 N
100 N
1600 N
For a given material, the Young s modulus is 2.4 times that of modulus ofrigidity.
Its Poisson s ratio is
0.3
0.1
0.2
0.4
1
2
3
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