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Applying NLM along 3 Axis

Two blocks of...

Question

Two blocks of masses $m_{1}$ and $m_{2}$ connected by a string are placed gently over a fixed inclined plane such that the tension in the connecting string is initially zero. The coefficient of friction between $m_{1}$ and inclined plane is $μ_{1}$ and between $m_{2}$ and the inclined plane is $μ_{2}$ . The tension in the string shall continue to remain zero if

A

μ_{1} > t a n α a n d μ_{2} < t a n β

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B

μ_{1} < t a n α a n d μ_{2} > t a n β

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C

μ_{1} > t a n α a n d μ_{2} > t a n β

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D

μ_{1} < t a n α a n d μ_{2} < t a n β

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Solution

The correct option is C $μ_{1} > t a n α a n d μ_{2} > t a n β$
For zero tension the maximum friction should be greater then downwards sliding force.
SO, $μ_{1} m g c o s α > m g s i n α \Rightarrow μ_{1} > t a n α$
Similarly, $μ_{2} > t a n β$

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Figure

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