Question

A cylinder of mass $m$ is suspended through two strings wrapped round it as shown in fig. Find the tension $T$ in the string and

• A. $\sqrt{\frac{4}{3}gh}$
• B. $\frac{mg}{3}$
• C. $\frac{mg}{2}$
• D. $mg$

Answer 1

The correct option is A $\sqrt{\frac{4}{3}gh}$

Net force $=mg-2T=ma$...........(1)

Net Torque $=2Tr=1cm-\frac{a}{r}$

$=2T=1cm-\frac{a}{r^2}$..........(2)

From (1) and (2)

$a=\frac{mg}{1+\frac{1cm}{r^2}}$

From (1) $T=\frac{1cm}{2r^2}\left[\frac{mg}{m+\frac{1cm}{r^2}}\right]$

Putting,

$1cm=\frac{1cm}{2r^2}m{r}^2$, we get

$a=\frac{2}{3}g$

$T=\frac{mg}{6}$

$v^2=2ah=2\left(\frac{2}{3}g\right)=h$

$v=\sqrt{\frac{4}{3}gh}$
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