question_answer

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. Find the location of P with respect to C

A)  \[\frac{4\ell }{3}\]

B)  \[\ell \]

C)  \[\frac{2\ell }{3}\]

D)  \[\frac{3\ell }{2}\]

Correct Answer: A

Solution :

For translational motion the force should be applied at the center of mass of the body Let the mass of AB be m, so the mass of vertical rod is 2 m. We can consider that the whole mass of a rod is placed at its center of mass \[\therefore \]Mass m is placed at\[{{y}_{1}}\]and mass 2 m is placed at\[{{y}_{2}}\] Hence, distance of combined center of mass from C \[=\frac{m.2l+2ml}{m+2m}=\frac{4}{3}l\] Hence, the correction option is [a].