Question

A solid uniform disk of mass m rolls without slipping down a fixed inclined plane with an acceleration a. The frictional force on the disk due to surface of the plane is?

• A. $2$ ma
• B. $3/2$ ma
• C. $ma/2$
• D. $1/2$ ma

Answer 1

The correct option is C $ma/2$

Here as the sphere is rolling down an inclined plane it will produce a torque $\tau =I\alpha$ where I = moment of inertia and $\alpha$=angular acceleration

Now the frictional force $f=N{\mu }_s$

Where N=normal force=$mg\cos \theta$ and ${\mu }_s$=static friction

We also know moment of inertia of sphere $I=\frac{1}{2}m{R}^2$;where R=radius of sphere.

and $\alpha =\frac{acceleration\left(a\right)}{R}$

In the given case torque$\tau$=frictional force$f\times R$

$fR=I\tau$

$fR=\frac{1}{2}m{R}^2\frac{a}{R}$

$f=\frac{ma}{2}$