In the arrangement shown, the end B of the rod of length ‘l’ is made to move with constant velocity V. Then velocity of its centre of mass when θ$$=300$$ is

Question

In the arrangement shown, the end B of the rod of length  ‘l’ is made to move with constant velocity V. Then velocity of its centre of mass when θ$$=300$$ is

Infinity Learn · Accepted Answer

O is the position of instantaneous centre of rotation. Then entire rod is rotating about O with angular velocity ω at that instantwhere ω $$=$$ vBOB  $$=$$  vl $$sin$$ θNow    $$OA2$$  $$+$$  $$OB2$$ $$=$$ $$2$$.  $$AC2$$  $$+$$  $$OC2$$⇒     $$l2$$ $$cos2$$θ  $$+$$  $$l2$$  $$sin2$$ θ  $$=$$  $$2$$ $$l24$$  $$+$$  $$OC2$$⇒   $$OC2$$  $$=$$ $$l22$$  −  $$l24$$ $$=$$  $$l24$$      ⇒   OC $$=$$ $$l2$$∴     vC $$=$$  ω . OC  $$=$$  vl  $$sin$$  θ  ×  $$l2$$  $$=$$  $$v2$$ $$sin$$ θWhen θ  $$=$$ $$300$$,   vC  $$=$$  $$v2$$ $$sin$$ $$300$$ $$=$$  v

In the arrangement shown, the end B of the rod of length ‘l’ is made to move with constant velocity V. Then velocity of its centre of mass when $θ = 30^{0}$ is

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In the arrangement shown, the end B of the rod of length ‘l’ is made to move with constant velocity V. Then velocity of its centre of mass when θ=300 is

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In the arrangement shown, the end B of the rod of length ‘l’ is made to move with constant velocity V. Then velocity of its centre of mass when $θ = 30^{0}$ is