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Two blocks of equal mass $m_{1} = m_{2} = 10 k g$ are connected to each other through massless and inextensible string that passes over a light frictionless pulley placed on a fixed stationary wedge as shown in the figure. Find the time taken (in seconds) by the block of mass $m_{1}$ to hit the pulley which is at a distance of $20 (\sqrt{3} - 1) m$ away from it at t=0 $(T a k e g = 10 m s^{- 2})$

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answer is 4.

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Detailed Solution

Equation of Motion for two blocks along the plane:

$m_{2} g \sin θ_{2} - T = m_{2} a$

$T - m_{1} g \sin θ_{1} = m_{1} a \Rightarrow a = \frac{m_{2} g \sin θ_{2} - m_{1} g \sin θ_{1}}{m_{1} + m_{2}} = \frac{\sqrt{3} - 1}{4} g$

Use $S = \frac{1}{2} a t^{2}$

Thus, time taken=4 s.

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