Given: A T-shaped object with dimensions shown in the figure is lying on a smooth floor. A force \\\\(\\vec F\\\\) is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. To find the location of P with respect to C.Solution:To have the required motion, the force \\\\(\\vec F\\\\) has to be applied at the center of mass.The point P must be the centre of mass of the T-shaped object since the force F does not produce any rotational motion of the object.The horizontal part of the T-shaped object has length L. If the mass of the horizontal portion is ‘m’, the mass of the vertical portion of the T- shaped object is 2m since its length is 2L. Therefore, the T-shaped object reduces to two point masses m and 2m at distances 2L and L respectively from the point C. The distance ‘r’ of the centre of mass of the system from the point C is given by\\\\(r=\\dfrac {m_1r_1+m_2r_2}{m_1+m_2}\\\\\\implies r=\\dfrac {m\ imes 2L+2m\ imes L}{m+2m}\\\\\\implies r=\\dfrac {4L}{3}\\\\)is the location of P with respect to C.