The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha$, the coefficient of linear expansion of vessel $B$ is
The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha$, the coefficient of linear expansion of vessel $B$ is
- A
$\frac{{\alpha {\gamma _1}{\gamma _2}}}{{{\gamma _1} + {\gamma _2}}}$
- B
$\frac{{{\gamma _1} - {\gamma _2}}}{{2\alpha }}$
- C
$\frac{{{\gamma _1} - {\gamma _2} + \alpha }}{3}$
- D
$\frac{{{\gamma _1} - {\gamma _2}}}{3} + \alpha $
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S.No.
$l(m)$
$\Delta T{(^o}C)$
$\Delta l(m)$
$(1)$
$2$
$10$
$4\times 10^{-4}$
$(2)$
$1$
$10$
$4\times 10^{-4}$
$(3)$
$2$
$20$
$2\times 10^{-4}$
$(4)$
$3$
$10$
$6\times 10^{-4}$
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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 $4$.
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