Question

A boy B drags a wedge A by an in extensible string passing over the pulleys 1,2,3 & 4 as shown in the figure . If all the pulleys are smooth and the boy walks with constant velocity of magnitude v, the magnitude of relative velocity between the boy and the wedge is equal to

• A. v
• B. 2v
• C. 2.5v
• D. 1.25v

Answer 1

Answer: (D)

1.25v

Writing the constraint equation from the pulley $4$,

$x+x+x+x+y=c$

differentiating with respect to time,we get

$4v_A-v_B=0$

$v_A=0.25v$

So, relative velocity w.r.t $B$ will be $v+0.25v$