Numerical : 1

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Four masses $m_1, m_2, m_3 \ and \ m_4$ are 200 kg, 300 kg, 240 kg and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45 $^{\circ}$, 75 $^{\circ}$ and 135 $^{\circ}$. Find the position and magnitude of the balance mass required, If its radius of rotation is 0.2 m.

$m_1 = 200 \ kg$	$r_1 = 0.2 \ m$	$f_{c1} = m_1\ r_1 = 40kg.m$
$m_2 = 300 \ kg$	$r_2 = 0.15 \ m $	$f_{c2} = m_2 \ r_2 = 45 \ kg.m$
$m_3 = 240 \ kg$	$r_3 = 0.25 \ m $	$f_{c3} = m_3 \ r_3 = 60 \ kg.m$
$m_4 = 260 \ kg $	$ r_4 = 0.3 \ m $	$f_{c4} = m_4 \ r_4 = 78 \ kg.m$
$m_b = \ ?$	$r_b = 0.2 \ m $

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