Question

A T shaped object with dimensions shown the figure, is lying on a smooth floor. F is applied at the point P parallel i A1/ , such that the object has only translational motion without rotation. Find the location of P with respect to C

• A. $\frac{2}{3}l$
• B. $\frac{3}{2}l$
• C. $\frac{4}{3}l$
• D. $l$

Answer 1

Answer: (C)

$\frac{4}{3}l$

$\begin{array}{c}\text{Let, mass of portion}AB\text{be}M\text{,}\\ \text{and mass of portion}CD\text{be}2M\text{.}\\ \text{Coordinates of centre of mass of}AB=(0,0)\end{array}$

$\begin{array}{c}\text{and coordinates of COM of CD=(0,-l)}\\ \text{Thus, coordinates of COM of system}=(0,\frac{0\times m-2m\ell }{3m})\\ =(0,-\frac{2}{3}l)\end{array}$

$\begin{array}{c}\text{Now, due to Force}F\text{, this particular system will attend only}\\ \text{translational motion only if point of application (P) is the centre of}\\ \text{mass of this system.}\\ \text{so,}P\text{is at}(2-\frac{2}{3})l=\frac{4}{3}\text{l distance from}C\text{.}\end{array}$