Question

A block of mass m slides down the plane inclined at angle \(30\degree\) with an acceleration \(\frac{g}{4}\). The value of the coefficient of kinetic friction will be:

• A. \(2\sqrt{3} - \frac{1}{2}\)
• B. \(\frac{1}{2\sqrt{3}}\)
• C. \(2\sqrt{3}+\frac{1}{2}\)
• D. \(\frac{\sqrt{3}}{2}\)

Hint:

For inclined plane problems:
• Use force components along and perpendicular to the plane.
• Solve for friction using acceleration and the force equation.

Answer 1

The Correct Option is B

1. Force Equation:

\[mg \sin 30^{\circ} - \mu mg \cos 30^{\circ} = ma.\]

2. Substitute Values: - \(a = \frac{g}{4}\), \(\sin 30^{\circ} = \frac{1}{2}\), \(\cos 30^{\circ} = \frac{\sqrt{3}}{2}\).

\[mg \frac{1}{2} - \mu mg \frac{\sqrt{3}}{2} = m \frac{g}{4}.\]

3. Solve for \(\mu\):

 

\[\frac{\sqrt{3}}{2}\mu=\frac{1}{4}\]

\[\mu=\frac{1}{2\sqrt{3}}\]