Two block are connected by a string as shown in the figure- If the coefficient of kinetic friction between the upper block and the surface is - and assuming that the pulley is massless and frictionless- The blocks are released from rest- their common speed after they have moved a distance L- is-

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Standard XII

Physics

Velocity

Two block are...

Question

Two block are connected by a string as shown in the figure. If the coefficient of kinetic friction between the upper block and the surface is $μ$ and assuming that the pulley is massless and frictionless. The blocks are released from rest, their common speed after they have moved a distance $L$ , is:

\sqrt{\frac{(m_{2} + μ m_{1}) g L}{(m_{1} + m_{2})}}

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\sqrt{2 g L}

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\sqrt{\frac{2 (m_{2} - μ m_{1}) g L}{(m_{1} + m_{2})}}

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\sqrt{\frac{(m_{2} - μ m_{1}) g L}{2 (m_{1} + m_{2})}}

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Solution

The correct option is C $\sqrt{\frac{2 (m_{2} - μ m_{1}) g L}{(m_{1} + m_{2})}}$
From work energy theorem
$m_{2} g L - μ m_{1} g L = \frac{1}{2} v^{2} (m_{1} + m_{2})$
$= \sqrt{\frac{2 (m_{2} - μ m_{1}) g L}{(m_{1} + m_{2})}}$

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Two blocks are connected by a string, as shown in the figure. They are released from rest. Find the speed after they have moved a distance x. $μ$ is the coefficient of kinetic friction between the upper block and the surface. Assume that the pulley is massless and frictionless.