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  4. A T shaped uniform density object with dimensions shown in the figure is lying on a smooth floor. A force overset arrow 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 . <style type=text/css><!-- @page margin: 2cm P margin-bottom: 0.21cm --> </style> <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-sptcp81infsjluem.jpg />

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Q. A $T$ shaped uniform density object with dimensions shown in the figure is lying on a smooth floor. A force $\overset{ \rightarrow }{F}$ 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 $C$ .
Question

NTA AbhyasNTA Abhyas 2022

Solution:

It is a case of translation motion without rotation. The force should act at the centre of mass
$Y_{ cm }=\frac{( m \times 2 l )+(2 m \times 1)}{ m +2 m }=\frac{4 l }{3}$
( considering point $C$ as origin )