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

Options

  1. Av
  2. Bv sin ⁡ θ
  3. Cv sin ⁡ θ
  4. Dv cos ⁡ θ ⁡

Correct answer

C. v sin ⁡ θ

Step-by-step solution

From geometry l 2 = x 2 + y 2 but y is constant, hence differentiating, we have, 2 l d l d t = 2 x d x d t But d l d t = v . Hence horizontal velocity of block, v x = d x d t ⇒ l v = x . v x or v x = l . v x = v sin ⁡ θ

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