Q.
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
A) $v$
B) $v\sin\theta$
C) $\frac{v}{\sin\theta}$
D) $\frac{v}{\cos{\theta\ }}$
Explanation
(c) From geometry $l^{2} = x^{2} + y^{2}$ but $y$ is constant, hence differentiating, we have, $2l\frac{dl}{dt} = 2x\frac{dx}{dt}$
But $\frac{dl}{dt} = v$. Hence horizontal velocity of block,
$v_{x} = \frac{dx}{dt}$
[image:5_image256.jpeg]
$\Rightarrow \ lv = x.v_{x}$ or $v_{x} = \frac{l.v}{x} = \frac{v}{\sin\theta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.