Question

A solid cylinder of mass \(m\) is wrapped with an inextensible light string and is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is: [The coefficient of static friction, \(\mu_s\), is 0.4] (Figure: Cylinder on 60° incline with string wrapped parallel to the incline) 

• A. \(\frac{mg}{5}\)
• B. \(5 mg\)
• C. \(\frac{7}{2} mg\)
• D. 0

Hint:

Check the net torque about the contact point. If the gravity component and the string tension cancel each other out, no friction is generated.

Answer 1

The Correct Option is D

Step 1: Analyze the forces. For a cylinder with a string wrapped around it on an incline, if the string is pulled or fixed such that it provides a specific torque, we check for equilibrium.
Step 2: In specific configurations where the string is fixed at the top, the tension \(T\) and the weight component \(mg \sin \theta\) can balance such that no friction is required for pure rolling or static equilibrium.
Step 3: Solving the torque and force balance equations for this specific geometry reveals that the system is in equilibrium with zero friction.