The coefficients of linear expansion of brass and steel rods are α1 and α2, lengths of brass and steel rods are l1 and l2 respectively. If (l2 - l1) is maintained the same at all temperatures, Which one of the following relations holds good?
1. α1l22 = α2l12
2. α12l2 = α22l1
3. α1l1 = α2l2
4. α1l2 = α2l1
The value of the coefficient of volume expansion of glycerin is \(5\times10^{-4}\) K-1. The fractional change in the density of glycerin for a temperature increase of \(40^\circ \mathrm{C}\) will be:
1. | \(0.015\) | 2. | \(0.020\) |
3. | \(0.025\) | 4. | \(0.010\) |
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. \(88~\text{cm}\)
When a uniform rod is heated, which of its following properties will increase as a result of it?
1. mass
2. weight
3. center of mass
4. moment of inertia
If two rods of length L and 2L having coefficients of linear expansion and respectively are connected so that their total length becomes 3L, the average coefficient of linear expansion of the composition of rods equals:
1.
2.
3.
4. none of these
A pendulum clock runs faster by 5 seconds per day at \(20^{\circ}\mathrm {C}\) and goes slow by 10 second per day at \(35^{\circ}\mathrm {C}\). It shows the correct time at a temperature of:
1. \(27.5^{\circ}\mathrm {C}\)
2. \(25^{\circ}\mathrm {C}\)
3. \(30^{\circ}\mathrm {C}\)
4. \(33^{\circ}\mathrm {C}\)
Two rods, one made of aluminium and the other made of steel, having initial lengths \(l_1\) and \(l_2\) are connected together to form a single rod of length . The coefficient of linear expansion for aluminium and steel are and respectively. If the length of each rod increases by the same amount when their temperature is raised by \(t^\circ \mathrm{C},\) then the ratio \(\frac{l_1}{l_1+l_2}\) is:
1.
2.
3.
4.
A bimetallic strip is shown in the figure. On cooling, which shape will it attain if
1. | 2. | ||
3. | 4. |
A large steel wheel is to be fitted onto a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the wheel's central hole has a diameter of 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft?
(Assume the coefficient of linear expansion of the steel to be constant over the required temperature range and \(\alpha\) steel = \(1.20 \times 10^{-5} K^{-1}\))
2. -70°C
3. -69°C
4. -67°C
The diagram shows a bimetallic strip used as a thermostat in a circuit. Copper expands more than Invar for the same temperature rise.
What will be switched on when the bimetallic strip becomes hot?
1. | bell only | 2. | lamp and bell only |
3. | motor and bell only | 4. | lamp, bell, and motor |