A rod P of length 1 m is hinged at one end A and there is a ring attached to other end. Another long

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3-2.Motion in Plane

hard

A rod $P$ of length $1\ m$ is hinged at one end $A$ and there is a ring attached to the other end. Another long rod $Q$ is hinged at $B$ and it passes through the ring. The rod $P$ is rotated about an axis which is perpendicular to plane in which both the rods are present and the variation between the angles $\theta$ and $\phi $ are plotted as shown. The distance between the hinges $A$ and $B$ is ....... $m$.

A$3$

B$2$

C$1$

D$0$

Solution

For maximum value of $\phi, \theta$ is $60^{\circ} .$ In this
situation rod $Q$ is tangent on the circle on which
ring attached to $P$ moves.
$l \cos 60=1$
$l=2 \mathrm{m}$

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