A simple pendulum made of a bob of mass $m$ and a metallic wire of negligible mass has time period $2s$ at $T = 0\,^oC$ . If the temeprature of the wire is increased and the corresponding change in its time peirod is plotted against its temperature, the resulting graph is a line of slope $S$. If the coefficient of linear expansion of metal is $\alpha $ then the value of $S$ is
A simple pendulum made of a bob of mass $m$ and a metallic wire of negligible mass has time period $2s$ at $T = 0\,^oC$ . If the temeprature of the wire is increased and the corresponding change in its time peirod is plotted against its temperature, the resulting graph is a line of slope $S$. If the coefficient of linear expansion of metal is $\alpha $ then the value of $S$ is
- [JEE MAIN 2016]
- A
$\frac {\alpha }{2}$
- B
$2\alpha $
- C
$\alpha $
- D
$\frac {1}{\alpha }$
Similar Questions
Write relation between coefficient of linear and volume expansion.
Write relation between coefficient of linear and volume expansion.
The scale on a steel metre stick is calibrated at $20^o\,C$.The error in the reading of $50\,cm$ at $30^o\,C$ is: (take linear expansion coefficient of steel $= 1.0 \times 10^{-5} / ^oC)$
The scale on a steel metre stick is calibrated at $20^o\,C$.The error in the reading of $50\,cm$ at $30^o\,C$ is: (take linear expansion coefficient of steel $= 1.0 \times 10^{-5} / ^oC)$
A student records the initial length $l$, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows :
S.No.
$l(m)$
$\Delta T{(^o}C)$
$\Delta l(m)$
$(1)$
$2$
$10$
$4\times 10^{-4}$
$(2)$
$1$
$10$
$4\times 10^{-4}$
$(3)$
$2$
$20$
$2\times 10^{-4}$
$(4)$
$3$
$10$
$6\times 10^{-4}$
If the first observation is correct, what can you say about observations $2,\,3$ and $4$.
A student records the initial length $l$, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows :
| S.No. | $l(m)$ | $\Delta T{(^o}C)$ | $\Delta l(m)$ |
| $(1)$ | $2$ | $10$ | $4\times 10^{-4}$ |
| $(2)$ | $1$ | $10$ | $4\times 10^{-4}$ |
| $(3)$ | $2$ | $20$ | $2\times 10^{-4}$ |
| $(4)$ | $3$ | $10$ | $6\times 10^{-4}$ |
If the first observation is correct, what can you say about observations $2,\,3$ and $4$.
If on heating liquid through $80°C$, the mass expelled is $(1/100)^{th}$ of mass still remaining, the coefficient of apparent expansion of liquid is
If on heating liquid through $80°C$, the mass expelled is $(1/100)^{th}$ of mass still remaining, the coefficient of apparent expansion of liquid is
A pendulum clock keeps correct time at $0°C$. Its mean coefficient of linear expansions is $\alpha /^\circ C$, then the loss in seconds per day by the clock if the temperature rises by $t°C$ is
A pendulum clock keeps correct time at $0°C$. Its mean coefficient of linear expansions is $\alpha /^\circ C$, then the loss in seconds per day by the clock if the temperature rises by $t°C$ is