Q. No.| Assertion (A): | The bridges are declared unsafe after long use. |
| Reason (R): | The bridges lose their elastic strength with time. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
The Young's modulus of a wire of length L and radius r is Y. If length is reduced to and radius to , then Young's modulus will be:
1.
2. Y
3. 2Y
4. 4Y
| Assertion (A): | An \(\mathrm{I} \text-\)shaped beam is preferred over a rectangular beam for supporting loads, such as traffic, on structures like bridges. |
| Reason (R): | An \(\mathrm{I} \text-\)shaped beam reduces weight without compromising the strength. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
| Assertion (A): | Elastomers are used as vibration dampers. |
| Reason (R): | Elastomers show elastic hysteresis. |
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is true but (R) is false. |
| 4. | Both (A) and (R) are false. |
When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increase in length will be:
1. 0.5 cm
2. 2 cm
3. 4 cm
4. 8 cm
As a ball falls into a lake with a depth of \(200~\text m,\) it experiences a decrease in volume of \(0.1 \text{%}\) at the bottom. The bulk modulus of the material of the ball is:
(take \(g=9.8~\text{m/s}^2\))
1. \(19.6\times10^{-10}~\text{N/m}^2\)
2. \(19.6\times10^{10}~\text{N/m}^2\)
3. \(19.6\times10^{-8}~\text{N/m}^2\)
4. \(19.6\times10^{8}~\text{N/m}^2\)
Young’s modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass, are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:
1. \(1:2\)
2. \(2:1\)
3. \(4:1\)
4. \(1:1\)
The load versus elongation graph for four wires, all of the same length and made from the same material, is shown in the figure. One of the lines corresponds to the thinnest wire.
Which line represents the thinnest wire?
1. \(OC\)
2. \(OD\)
3. \(OA\)
4. \(OB\)
The Marina trench is located in the Pacific Ocean, and at one place it is nearly \(11 \) km beneath the surface of the water. The water pressure at the bottom of the trench is about \(1.1 \times10^8\) Pa. A steel ball of initial volume \(0.32\) m3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom? (Given: \(B_{\mathrm{steel}}=1.6 \times10^{11}\) N/m2)
| 1. | \(1.01\times10^{-3}\) m3 | 2. | \(2.2 \times10^{-4}\) m3 |
| 3. | \(1.9 \times10^{-3}\) m3 | 4. | none of these |
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