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Question

A triangular set square of angle 30,60 and 90 and of negligible mass is suspended freely from the right-angle corner and weights are hung at the two corners. If the hypotenuse of the set square adjust horizontally, then the ratio of the weights W1W2 is 1:n. The value of n is (integer only)


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Solution

The hypotenuse will be oriented horizontally only when torque on the hypotenuse becomes zero.

Using, principle of moments,

Clockwise torque about point D = Anticlockwise torque about point D

W2(BD)=W1(AD)

W1W2=BDAD .......(1)


Now, From the diagram,

Let AB=l

AC=lcos30 ; BC=lcos60

AD=ACcos30=lcos230

BD=BCcos30=lcos260

Putting this values in (1) we get,

W1W2=BDAD=cos260cos230=1434=13

Hence, n=3
Why this question ?

This question involves idea of rotational equilibrium, when object is in rotational equilibrium, net clockwise torque and net anticlockwise torque about axis of rotation will be equal.



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