Question

Two blocks of masses $m_1=m_2=m$, are connected by a string of negligible mass which passes over a frictionless pulley connected with plane as shown in the figure. When the angle of inclination is $\theta ={30}^o$, then the mass $m_1$ just begins to move up the inclined plane. What is the coefficient of friction between block $m_1$ and the inclined plane?

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{2\sqrt{2}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{2\sqrt{3}}$

Answer 1

The correct option is C $\frac{1}{\sqrt{3}}$

To just begin to slide up the friction will be kinetic friction

Applying free body diagram on blocks
$m_{1}gsin{30}^o+\mu m_{1}gcos{30}^o=m_{2}g$
$m_1=m_2=m$
$\Rightarrow \frac{mg}{2}+\mu mg\frac{\sqrt{3}}{2}=mg$
$\Rightarrow \mu =\frac{1}{\sqrt{3}}$