Question

A uniform thin flat isolated disc is floating in space. It has radius $R$ and mass $m$. A force $F$ is applied to it at a distance $d=\frac{r}{2}$ from the centre in the y-direction. Treat this problem as two-dimensional. Just after the force is applied :

• A. acceleration of the centre of the disc is $\frac{F}{m}$.
• B. angular acceleration of the disk is $\frac{F}{mR}$.
• C. acceleration of leftmost point on the disc is zero.
• D. point which is instantaneously unaccelerated is the rightmost point.

Answer 1

Answer: (A), (B), (C)

acceleration of the centre of the disc is $\frac{F}{m}$.
angular acceleration of the disk is $\frac{F}{mR}$.
acceleration of leftmost point on the disc is zero.

Using Newtons second law we have $F=ma$
or
$a=\frac{F}{m}$
Thus option A is correct.
Using torque balance we have
$F\frac{R}{2}=\frac{1}{2}m{R}^2\alpha$
or
$\alpha =\frac{F}{mR}$
Thus option B is correct
$aP=a-\alpha R=0$
Now acceleration at point P
$a_P=a-\alpha R$ which equals zero.
Thus option C is also correct.