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
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 $4$.
Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at $0^o C$ while the tube on the right is kept at $30^o C$ in a water bath. The difference in the levels of the liquid in the two tubes is $4 \,\,cm$ while the height of the liquid column at $0^o C$ is $120\,\,cm$. The coefficient of volume expansion of liquid is (Ignore expansion of glass tube)
Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at $0^o C$ while the tube on the right is kept at $30^o C$ in a water bath. The difference in the levels of the liquid in the two tubes is $4 \,\,cm$ while the height of the liquid column at $0^o C$ is $120\,\,cm$. The coefficient of volume expansion of liquid is (Ignore expansion of glass tube)
A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is $\alpha$ and the coefficient of volume expansion of liquid is $\gamma$. On increasing the temperature of (liquid + cube) system, the cube will sink if
A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is $\alpha$ and the coefficient of volume expansion of liquid is $\gamma$. On increasing the temperature of (liquid + cube) system, the cube will sink if
Density of substance at $0°C$ is $10\, gm/cc$ and at $100°C,$ its density is $9.7\, gm/cc$. The coefficient of linear expansion of the substance will be
Density of substance at $0°C$ is $10\, gm/cc$ and at $100°C,$ its density is $9.7\, gm/cc$. The coefficient of linear expansion of the substance will be
The loss in weight of a solid when immersed in a liquid at $0^o C$ is $W_0$ and at $t^o C$ is $W$. If cubical coefficient of expansion of the solid and the liquid by $\gamma_s$ and $\gamma_l$ respectively, then $W$ is equal to :
The loss in weight of a solid when immersed in a liquid at $0^o C$ is $W_0$ and at $t^o C$ is $W$. If cubical coefficient of expansion of the solid and the liquid by $\gamma_s$ and $\gamma_l$ respectively, then $W$ is equal to :