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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?
985741_0013afb80fb04545ab44088414cdda80.png


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

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

1235182_985741_ans_b28146273b6640bb835713cb392a9162.png

Physics

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