Question

A T shaped object, having uniform linear mass density, with dimension shown in the figure is lying on a smooth floor. A force $F$ is applied at the point P parallel to AB, such that the object has only translational motion without rotation. The distance of P with respect to C is

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

Answer 1

The correct option is A $\frac{4l}{3}$

For pure translational motion, the force F should act at centre of mass
$Y_{cm}=\frac{m\left(2l\right)+2\left(m\right)l}{3m}=\frac{4l}{3}$
$\therefore \left(a\right)$

Why this question? "When net force on a body is acting at its COM, it translates." "If there is an axis along which there is symmmetry, COM exists on that axis"