A uniform rod of length \( 200 \mathrm{~cm} \) and mass \( 500 \mathrm{~g} \) is balanced on a w....

A uniform rod of length \( 200 \mathrm{~cm} \) and mass \( 500 \mathrm{~g} \) is balanced on a wedge placed at \( 40 \mathrm{~cm} \) mark. A mass
\( \mathrm{P} \)
of \( 2 \mathrm{~kg} \) is suspended from the rod at \( 20 \mathrm{~cm} \) and
W
another unknown mass \( m \) is suspended from the rod at \( 160 \mathrm{~cm} \) mark as shown in the figure. Find the value of \( m \) such that the rod is in equilibrium.
\[
\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)
\]
(1) \( \frac{1}{2} \mathrm{~kg} \)
(2) \( \frac{1}{3} \mathrm{~kg} \)
(3) \( \frac{1}{6} \mathrm{~kg} \)
(4) \( \frac{1}{12} \mathrm{~kg} \)