Q.

A block is dragged on a smooth plane with the help of a rope which with a velocity v as shown in fig. The horizontal velocity of the block is

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a

v

b

v/sin⁡θ

c

v sin⁡θ

d

v/cos⁡θ

answer is B.

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Detailed Solution

See fig. The angle 0 and lengths l vary with time.Let at any instant, the length AB be /. Thenx2+y2=l2 or 2xdxdt+2ydydt=2ldldtThere is no vertical motion of the block. So,dydt=0,dxdt=Vx and dldt=V∴2xVx=2lv or vx=lxvor vx=v(x/l)=Vsin⁡θ.
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A block is dragged on a smooth plane with the help of a rope which with a velocity v as shown in fig. The horizontal velocity of the block is