The ratio of lengths of two rods \(A\) and \(B\) of the same material is \(1:2\) and the ratio of their radii is \(2:1\). The ratio of modulus of rigidity of \(A\) and \(B\) will be:
1. | \(4:1\) | 2. | \(16:1\) |
3. | \(8:1\) | 4. | \(1:1\) |
When a spiral spring is stretched by suspending a load on it, the strain produced is called:
1. | Shearing |
2. | Longitudinal |
3. | Volume |
4. | shearing and longitudinal |
The Young's modulus of the material of a wire is \(6\times 10^{12}~\text{N/m}^2\) and there is no transverse strain in it, then its modulus of rigidity will be:
1. \(3\times 10^{12}~\text{N/m}^2\)
2. \(2\times 10^{12}~\text{N/m}^2\)
3. \(10^{12}~\text{N/m}^2\)
4. None of the above
Modulus of rigidity of a liquid:
(1) Non zero constant
(2) Infinite
(3) Zero
(4) Can not be predicted
A cube of aluminium of sides \(0.1~\text{m}\) 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 bottom face. The shearing strain would be:
1. \(0.02\)
2. \(0.1\)
3. \(0.005\)
4. \(0.002\)
The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30°. Then angle of shear is
(1)
(2)
(3)
(4)
A rod of length l and radius r is joined to a rod of length l/2 and radius r/2 of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of , the twist angle at the joint will be
(a) (b)
(c) (d)
Shearing stress causes a change in-
(1) Length
(2) Breadth
(3) Shape
(4) Volume
To break a wire, a force of is required. If the density of the material is , then the length of the wire which will break by its own weight will be -
(a) 34 m (b) 30 m
(c) 300 m (d) 3 m
One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(S\) is the area of cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W_1}{S}\)
2. \(\frac{W_1+\left(\frac{W}{4}\right)}{S}\)
3. \(\frac{W_1+\left(\frac{3W}{4}\right)}{S}\)
4. \(\frac{W_1+W}{S}\)