Question

A T-shaped object with dimensions shown in the 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 transitional motion without rotation. Find the location of P with respect to C:

• A. $\frac{41}{3}$
• B. $1$
• C. $\frac{21}{3}$
• D. $\frac{31}{2}$

Answer 1

The correct option is A $\frac{41}{3}$

As the form is inform assume $i$ length of for has a mass $m$

Only if the Force $F$ as applied at the center of mass of the object will the object move translationally without rotation

The center of mass of $AB\left(l\right)$ is at is geometrical center and same for section $2l$

Length $l$ will have mass $m$

Length $2l$ will have mass $2m$

The $y$ location of center of mass:

$Ycm=\frac{2m\times l+m\times 2l}{(2m+m)}=\frac{4ml}{3m}=\frac{4l}{3}$

Ans : $A$