Let tension be $T$
$f_1=\sqrt{\frac{T}{\mu}} \times \frac{1}{2 l}=256$
$f_2=\sqrt{\frac{T+10}{\mu}} \times \frac{1}{2 l}=320$
$\sqrt{\frac{T}{T+10}}=\frac{256}{320}$
$\frac{T}{T+10}=\frac{(16)^2}{(16)^2 \times(20)^2}$
or $\frac{T}{T+10}=\frac{16^2}{(20)^2}$
or $400 T=256 T^2+2560$
or $144 T=2560$
or $T=\frac{2560}{144}$
or $T=\frac{2560}{16 \times 9}$
or $T=\frac{160}{9}$ Newton
$=\frac{16}{9} \,kg -w t$
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| List $I$ | List $II$ |
| $A$ Isothermal Process | $I$ Work done by the gas decreases internal energy |
| $B$ Adiabatic Process | $II$ No change in internal energy |
| $C$ Isochoric Process | $III$ The heat absorbed goes partly to increase internal energy and partly to do work |
| $D$ Isobaric Process | $IV$ No work is done on or by the gas |
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