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Physics-

General

Easy

Question

A $T$ shaped object with dimension shown in the figure, is lying on a smooth floor. A force $F$ is applied at the point $P$ parallel to $A B$ , such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$ .

$\frac{2}{3} l$
$\frac{3}{2} l$
$\frac{4}{3} l$
$l$

The correct answer is: $fraction numerator 4 over denominator 3 end fraction l$

For translator motion the force should be applied on the centre of mass of the body so we have to calculate the location of centre of mass of $T$ shaped object.
Let mass of rod $A B$ is $m$ so the mass of rod $C D$ will be 2 $m$ .
Let $y subscript 1 end subscript$ is the centre of mass of rod $A B$ and $y subscript 2 end subscript$ is the centre of mass of rod $C D$ . We can consider that whole mass of the rod is placed at their respective centre of mass $i e$ , mass $m$ is placed at $y subscript 1 end subscript$ and mass $2 m$ is placed at $y subscript 2 end subscript$ .
Taking point $c$ at the origin position vector of points $y subscript 1 end subscript a n d blank y subscript 2 end subscript$ can be written as
$r subscript 1 end subscript equals 2 l j comma blank r subscript 2 end subscript equals l j$
and $m subscript 1 end subscript equals m a n d m subscript 2 end subscript equals 2 m$
Position vector of centre of mass of the system
$r subscript C M end subscript equals fraction numerator m subscript 1 end subscript r subscript 1 end subscript plus m subscript 2 end subscript r subscript 2 end subscript over denominator m plus m subscript 2 end subscript end fraction equals fraction numerator m 2 l stack j with hat on top plus 2 m l stack j with hat on top over denominator m plus 2 m end fraction equals fraction numerator 4 m l stack j with hat on top over denominator 3 m end fraction equals fraction numerator 4 l stack j with hat on top over denominator 3 end fraction$

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