Question

A horizontal plank is $10.0m$ long with uniform density and mass $10kg$. It rests on two supports which are placed $1.0m$ from each end as shown in the figure. A man of mass $80kg$ can stand upto distance $x$ on the plank without causing it to tip. The value of $x$ is:

• A. $\frac{1}{2}m$
• B. $\frac{1}{4}m$
• C. $\frac{3}{4}m$
• D. $\frac{1}{8}m$

Answer 1

The correct option is A $\frac{1}{2}m$

The plank wont tip as long as the whole COM of the system remains in between the two supports. As the man moves towards the right, COM shifts towards right. Maximum distance to which he can move right will be when the COM is right on top of the the right support.
COM of plank lies on the geometric centre on the plank, i.e; 4m leftwards of the right support.
$4\times 10-80\times X=0$
or, $80X=40$
or, $X=1/2m$.