First slide

Connected bodies

Question

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

Moderate

A

$ν$
B

$\frac{v}{\sin θ}$
C

$vsin θ$
D

$\frac{v}{\cos θ}$

Solution

$\begin{aligned} L^{2} = x^{2} + y^{2} \\ ∴ y = constant \end{aligned}$
$\begin{aligned} 2 L \frac{dL}{dt} = 2 x \frac{dx}{dt} \\ \Rightarrow \frac{dx}{dt} = \frac{L}{x} V \end{aligned}$
Horizontal velocity $v_{x} = \frac{v}{\sin θ}$
$\frac{x}{L} = \sin θ$
or $v_{x} = \frac{V}{\sin θ}$

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