Question

# 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 $$\mu$$. What should be the minimum mass $$M_2$$ so that the block $$M_1$$ slides upwards?

A
M2=M1(sinθ+μcosθ)
B
M2=M1(sinθμcosθ)
C
M2=M1sinθ+μcosθ
D
M2=M1sinθμcosθ

Solution

## The correct option is A $$M_2 = M_1 ( sin\theta + \mu cos\theta)$$From above FBD$$\begin{array}{l} T=\mu { M_{ 1 } }g\cos \theta +{ M_{ 1 } }g\sin \theta \\ { M_{ 2 } }g\ge T \\ { M_{ 2 } }g\ge \mu { M_{ 1 } }g\cos \theta +{ M_{ 1 } }g\sin \theta \\ { M_{ 2 } }\ge { M_{ 1 } }\left( { \mu \cos \theta +\sin \theta } \right) \\ Hence, \\ option\, \, A\, \, is\, \, correct\, \, answer. \end{array}$$Physics

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