KVPY SA Exam 2015 Question Paper

Question : 68 of 80

Marks: +1, -0

A rigid body in the shape o f a “V” has two equal arms made of uniform rods. What must'the angle between the two rods be so that when the body is suspended from one end, the other arm is horizontal?

$\cos^{-1}(1/3)$
$\cos^{-1}(1/2)$
$\cos^{-1}(1/4)$
$\cos^{-1}(1/6)$

Validate

Solution:

When CM of system and Hinged point lie on one line then only system can remain in equilibrium in given position.

AB = l \cosθ

AP = l/2 \cosθ/2

\cosθ/2={AB}/{AP}

⇒AB=AP\cosθ/2

l \cosθ=l/2 \cos^2θ/2

2 \cosθ ={1+\cosθ}/2

4\cosθ = 1 +\ cosθ

3\cosθ = 1

\cosθ =1/3⇒θ=\cos^{-1} (1/3)

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