A T shaped object with dimensions shown in 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. Find the location of P with respect to C

Options

A. l
B. `(4)/(3)`l
C. `(3)/(2)` l
D. `(2)/(3)` l

Answer

B

Explanation

It is a case of translatory motion without rotation . Therefore the force should act at the centre of mass . Let `mu` be mass per unit length .
Then mass of AB `,m_(1) = mul` acts as O
Mass of OC , `m_(2) = mu (2l)` acts at D , where CD = l
Let DP = x
As P is the centre of the mass , therefore at equilibrium , `mu (l - x) = 2 mu l x`
`3x = l` or `x = (l)/(3)`
`therefore CP = CD + DP = l + (l)/(3) = (4l)/(3)`