question_answer

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

A)  \[\frac{\sqrt{5}\,mg}{M+\sqrt{5}\,m\,+2\,\mu \,m}\]      

B)  \[\frac{2\,mg}{m+5\,M\,+2\,\mu \,m}\]

C)  \[\frac{2\sqrt{5}\,mg}{M+5\,M\,+2\,\mu \,m}\]

D) \[\frac{5\sqrt{2}\,mg}{M+\sqrt{5}\,m\,+\sqrt{2}\,\mu \,m}\]

Correct Answer: C

Solution :

From the constraint net acceleration \[m=\sqrt{{{a}^{2}}+{{\left( 2a \right)}^{2}}}\,=\sqrt{5}a\]

\[mg=T-\mu N=2ma\]

\[N=ma\]

\[2T=\left( M+m \right)a\]