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A massless rod of length ' 2l ' leans against a frictionless wall and the surface is smooth. This rod is fitted with two point masses, each of mass 'm' at its end. If this rod starts sliding on the floor, find the equation of trajectory for its centre of mass. [Assume 'O' as origin, x axis along the surface, Y axis along the wall]

Option: 1
$x^{2}-y^{2}=l^{2}$

Option: 2
$x^{2}+y^{2}=4 l^{2}$

Option: 3
$x^{2}+y^{2}=l^{2}$

Option: 4
$x^{2}+2 y^{2}=4 l^{2}$

Answers (1)

best_answer

In $\triangle P Q R$ ,

$Q R=(2 l) \sin \alpha \\$

$S T=Q S \sin \alpha \\$

$S U=Q S \cos \alpha \\$

$Q S=\frac{P R}{2}=l$

$ST=l \sin \alpha=x_{0} \\$

$SU=l \cos \alpha=y_{0} \\$

$x_{0}^{2}+y_{0}^{2}=l^{2} \\$

$\Rightarrow r=l \\$

$x^{2}+y^{2}=l^{2}$

Posted by

Deependra Verma

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