Q. A T shape with dimensions shown in Figure is lying on a smooth floor. A force $\overrightarrow{F}$ is applied at the point $P$ parallel to $AB$, such that the object has only the translation motion without rotation. Find the location of $P$ with respect to $C$ Dd
A) $l$
B) $\frac{4}{3}l$
C) $\frac{3}{2}l$
D) $\frac{2}{3}l$
Explanation
(b) The object will have translation motion without rotation, when force $F$ is applied at the centre of mass of system. If $m$ is mass per unit length, the mass of $AB,\ m_{1} = ml$ at $O$ and mass of $OC$, $m_{2} = m(2l)$ at $D,$ where $CD = l$
Dd
Let $DP = x$
As $P$ is the centre of mass, therefore
$ml(l - x) = 2mlx$
$3x = l:x = l/3$
$\therefore CP = CD + DP = l + \frac{l}{3} = \frac{4l}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.