Two blocks of masses $M_{1}$ and $M_{2}$ are connected with a string which passes over a smooth pulley. The mass $M_{1}$ is placed on a rough incline plane as shown in Fig. The coefficient of friction between the block and the inclined planes is $μ$ . What should be the minimum mass $M_{2}$ so that the block $M_{1}$ slides upwards?

M_{2} = M_{1} (s i n θ + μ c o s θ)

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M_{2} = M_{1} (s i n θ - μ c o s θ)

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M_{2} = \frac{M_{1}}{s i n θ + μ c o s θ}

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M_{2} = \frac{M_{1}}{s i n θ - μ c o s θ}

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Solution

The correct option is A $M_{2} = M_{1} (s i n θ + μ c o s θ)$
From above FBD
$\begin{matrix} T = μ M_{1} g cos θ + M_{1} g sin θ M_{2} g \geq T M_{2} g \geq μ M_{1} g cos θ + M_{1} g sin θ M_{2} \geq M_{1} (μ cos θ + sin θ) H e n c e, o p t i o n A i s c o r r e c t a n s w e r . \end{matrix}$

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