A bob of mass 1kg is hanging from an inextensible massless string of length 2m. The string is pulled slowly at the midpoint to the left so that both portions of string are taut. The midpoint is now held at 0.5m away from the original vertical positon by a horizontal force. The same experiment is repeated, but with a hinged massless rod replacing the string:-

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The force required to hold the midpoint is larger in second case.

The tension in the string between the midpoint and the hinge is less than the tension in the rod between the midpoint and the hinge.

The tension in the string between the midpoint and the bob is more than the tension in the rod between the midpoint and the bob.

The force required to hold the midpoint is same in both cases.

answer is B, C.

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Detailed Solution

Question Image
$T_{1} \cos 30^{\circ} = m g$
$T_{1} = \frac{2 m g}{\sqrt{3}}$
$T_{2} = m g$
$F = T_{1} \sin 30^{\circ} = \frac{m g}{\sqrt{3}}$

$F' \times 1 \cos 30^{\circ} = m g \times 2 \sin 30^{\circ}$
$F'' = \frac{2 m g}{\sqrt{3}}$
$T_{2}^{'} = m g \cos 30^{0} = \frac{m g \sqrt{3}}{2}$
$T_{1}^{'} = F' \cos 60 = \frac{m g}{\sqrt{3}}$