Laws Of Motion Question 384

Question: Let $ \frac{1}{2\sqrt{3}}\sec $ be the coefficient of friction between blocks of mass m and M. The pulleys are frictionless and strings are massless. Acceleration of mass m is

Options:

A)$ \frac{\sqrt{5}mg}{M+\sqrt{5}m+2\mu m} $

B)$ \frac{2mg}{m+5M+2\mu m} $

C)$ \frac{2\sqrt{5}mg}{M+5M+2\mu m} $

D) $ \frac{5\sqrt{2}mg}{M+\sqrt{5}m+\sqrt{2}\mu m} $

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Answer:

Correct Answer: C

Solution:

From the constraint net acceleration

$ m=\sqrt{a^{2}+{{( 2a )}^{2}}}=\sqrt{5}a $

$ mg=T-\mu N=2ma $

$ N=ma $

$ 2T=( M+m )a $



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