A stone of mass 1 kg is tied at one end of a string of length 2m & is whirled in a horizontal circle if the string can with stand a maximum tension of 64N then the permissible maximum number of rotations per minute is

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$19$

$\frac{60}{π}$

$\frac{153 π}{3}$

$\frac{120 \sqrt{2}}{π}$

answer is D.

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Detailed Solution

m=1 kg
L= 2m
F=64 N W= $\frac{2 n π}{T} r a d / s$
$F = \frac{m v^{2}}{r} = m r w^{2}$
$W = \sqrt{\frac{64}{(1) (2)}} = \sqrt{\frac{64}{2}} = \sqrt{32} = 4 \sqrt{2}$
$\frac{n}{T} = \frac{4 \sqrt{2} X 30}{π} = \frac{120 \sqrt{2}}{π}$

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