A uniform rod of mass m and length l is suspended by means of two light inextensible strings as shown in fig. Tension in one string immediately after the other string is cut is mgn , Then the value of n is:

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A uniform rod of mass m and length l is suspended by means of two light inextensible strings as shown in fig. Tension in one string immediately after the other string is cut is $\frac{mg}{n}$ , Then the value of n is:

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answer is 4.

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Detailed Solution

When the string is cut (at end B ), the rod will rotate about end A .

Considering torque about A, and the angular acceleration of the centre of mass

$mg (\frac{1}{2}) = Iα mg (\frac{1}{2}) = (\frac{{ml}^{2}}{3}) \frac{a}{\frac{l}{2}}$

$\Rightarrow a = \frac{3}{4} g$

Also,

$T = mg - ma = mg - m (\frac{3}{4} g) = \frac{mg}{4}$

$\Rightarrow n = 4$

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