A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force `'vecF'` is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect C.

Options

A. `2/3 I`
B. `3/2 I`
C. `4/3 I`
D. I

Answer

C

Explanation

For pure translatory motion, not torque about centre of mass should be zero. Thus, F is applied at centre of mass of system.

`OP = (m_(1) xx 0 + m_(2) xx 1)/(m_(1) + m_(2))`
Where, `m_(1)` and `m_(2)` are masses of horizontal and vertical section of the object. Assuming objects is uniform.
`m_(2) = 2m_(1) rArr OP =(21)/3`
`PC = (1-(21)/3 + 1) = (21 -21/3) = 41/3`