JEE MAIN - Physics (2018 - 15th April Morning Slot - No. 23)
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A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod horizontal, a mass $$m$$ is suspended from its end $$A.$$A$$ set of $$(m,x)$$ values is recorded. The appropriate variables that give a straight line, when plotted, are :
$$m,x$$
$$m,{1 \over x}$$
$$m,{1 \over {{x^2}}}$$
$$m,{x^2}$$
Explanation
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Here, let the length of the rod is = $$\ell $$ and mass = m.
In equilibrium, torque about point of suspension x,
mg x = $$\left( {{\ell \over 2} - x} \right)Mg$$
$$ \Rightarrow \,\,\,\,$$ mx = M$${\ell \over 2}$$ $$-$$ mx
$$ \Rightarrow \,\,\,\,$$ m = $$\left( {{{m\ell } \over 2}} \right){1 \over x} - M$$
Comparing this straight line equation, y = mx + c
This is a straight line equation when we plot with variable m and $${1 \over x}$$.
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