In the arrangement shown in the figure at a particular instant, the roller is coming down with a speed of $$12$$ m $$s-1$$ and C is moving up with $$4$$ $$ms-1$$. At the same instant, it is also known that w.r.t. pulley P, $$blockr4$$ is moving down with speed $$3$$ $$ms-1$$. Determine the motion of block B (velocity) w.r.t. ground.

Question

Infinity Learn · Accepted Answer

Using constraint theory,$$l1+l2+l3=$$ constant ⇒$$v1+2v2+v3=0Take$$ downward as positive and upward as $$-ve$$. So $$12+2($$−$$4)+v3=0v3=$$ velocity of pulley $$P=$$−$$4ms$$−$$1=4ms$$−$$1$$ in upward direction v→$$AP=$$−v→BP⇒ v→$$AP=$$−v→B−v→Pv→$$B=v$$→P−v→$$AP=$$−$$4$$−$$(3)=$$−$$7ms$$−$$1i$$.e., block B will moves up with speed $$7$$ $$ms-1$$.

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