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Two blocks of masses m₁ and m₂ connected by a non-deformed light spring rest on a rough ground as shown in figure. If friction coefficient on ground is $μ$ then find the minimum constant force F to be applied on m₂ so that m₁ start sliding.

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$F = μg (m_{2} + \frac{m_{1}}{2})$

$F = μg (m_{2} + \frac{m_{1}}{3})$

$F = μg (m_{2} + \frac{m_{1}}{10})$

$F = μg (m_{2} + \frac{m_{1}}{8})$

answer is A.

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Detailed Solution

m₁will slide if spring force $kx \geq μ m_{1} g$
By work energy theorem m₂ is displaced by x
$0 + F x - {μm}_{2} g x - \frac{1}{2} {kx}^{2} = 0 F = {μm}_{2} g + \frac{1}{2} {μm}_{1} g F = μg (m_{2} + \frac{m_{1}}{2})$

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