JEE MAIN - Physics (2005 - No. 36)
A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $$'\,\,\overrightarrow F \,\,'$$ 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 $$C.$$
$${3 \over 2}L$$
$${2 \over 3}L$$
$$L$$
$${4 \over 3}L$$
Explanation
This is a case of translation motion without rotation, the force $$\overrightarrow F $$ has to be applied at center of mass.
i.e. the point $$'P'$$ has to be at the centre of mass
$$y = {{{m_1}{y_1} + {m_2}{y_2}} \over {{m_1} + {m_2}}}$$
$$ = {{m \times 2\ell + 2m \times \ell } \over {3m}}$$
$$ = {{4\ell } \over 3}$$
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