Question

A uniform disc is acted by two equal forces of magnitude $F$. One of them, acts tangentially to the disc, while other one is acting at the central point of the disc. The friction between disc surface and ground surface is $nF$. If $r$ be the radius of the disc, then the value of $n$ would be (in N) :

• A. 0
• B. 1.2
• C. 2
• D. 3.2

Answer 1

The correct option is A 0

As evident from the question we shall formulate the equation for linear and angular acceleration separately.

Linear equation of motion :

$2F-nF=ma$ ...........(1)

where $nF$ is friction and $a$ is linear acceleration.

Angular equation of motion : ${\tau }_o=I\alpha$

Moment of inertia of disc about point O $I=0.5m{r}^2$

$(F+nF)r=0.5m{r}^2\alpha$

where $\alpha$ is angular acceleration.

Also we know $a=r\alpha$

We get $(F+nF)=0.5ma$ ............(2)

From equation (1) - 2 x equation (1), we get $-3nF=0$

$⟹n=0$

Hence, the value on $n$ is $0$.