A smooth rod of length l is kept inside a trolley at an angle θ as shown in figure. What should be

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6.System of Particles and Rotational Motion

hard

A smooth rod of length $l$ is kept inside a trolley at an angle $\theta$ as shown in the figure. What should be the acceleration a of the trolley so that the rod remains in equilibrium with respect to it?

A

$g\, tan\theta$

B

$g\, cos\theta$

C

$g\, sin\theta$

D

$g\, cot\theta$

Solution

$F B D$ of rod $w.r.t.$ trolley

$N_{1}=m g \ldots(i)$

$N_{2}=m g \ldots(ii)$

Net torque about point $C=0$ $\therefore N_{1}=\left(\frac{1}{2} \sin \theta\right)=N_{2}=\left(\frac{1}{2} \cos \theta\right)$

or $(m a)(\sin \theta)=(m g)(\cos \theta)$

$\Rightarrow a=g \cot \theta$

Standard 11

Physics

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