A copper rod of \(88\) cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is:
\(\left(\alpha_{Cu}= 1.7\times10^{-5}~\text{K}^{-1}~\text{and}~\alpha_{Al}= 2.2\times10^{-5}~\text{K}^{-1}\right)\)
| 1. | \(68~\text{cm}\) | 2. | \(6.8~\text{cm}\) |
| 3. | \(113.9~\text{cm}\) | 4. | \(88~\text{cm}\) |
| 1. | \(\alpha_1L_2^2=\alpha_2L_1^2\) | 2. | \(\alpha_1^2L_2=\alpha_2^2L_1\) |
| 3. | \(\alpha_1L_1=\alpha_2L_2\) | 4. | \(\alpha_1L_2=\alpha_2L_1\) |
The value of the coefficient of volume expansion of glycerine is \(5\times10^{-4}~\text{K}^{-1}.\) The fractional change in the density of glycerine for a rise of \(40^\circ \text{C}\) in its temperature is:
| 1. | \(0.015\) | 2. | \(0.020\) |
| 3. | \(0.025\) | 4. | \(0.010\) |