The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\) N and \(b\) metre when the longitudinal tension is \(5\) N. The length of the string in metre when the longitudinal tension is \(9\) N will be:
1. | \(a-b\) | 2. | \(5b-4a\) |
3. | \(2b-\frac{1}{4}a\) | 4. | \(4a-3b\) |
Hooke's law is applicable for:
1. | elastic materials only | 2. | plastic materials only |
3. | elastomers only | 4. | all of these |
Two wires of copper having length in the ratio of \(4:1\) and radii ratio of \(1:4\) are stretched by the same force. The ratio of longitudinal strain in the two will be:
1. | \(1:16\) | 2. | \(16:1\) |
3. | \(1:64\) | 4. | \(64:1\) |
The length of elastic string, obeying Hooke's law is \(l_1\) metres when the tension is \(4~\text{N}\), and \(l_2\) metres when the tension is \(5~\text{N}\). The length in metres when the tension is \(0~\text{N}\) will be:
1. \(5l_1-4l_2\)
2. \(5l_2-4l_1\)
3. \(9l_1-8l_2\)
4. \(9l_2-8l_1\)
Given below are two statements:
Assertion (A): | Hooke's law is applicable up to the elastic limit. |
Reason (R): | Up to the elastic limit, stress is directly proportional to strain. |
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. |