Question

 A faulty balance of unequal arms and pans of unequal weights is used to find the true weight of a metal. By double weighing the weights are found to be 1210 g and 1000 g. Calculate the true weight of the metal.

Answer 1

(m_L  + 1210) x = (m_R + m_o) y ..............(1)

(m_L + m₀) x = (m_R + 1000) y .............(2)

m_L x = m_R y                           ..............(3)

Equations when the two pans are empty from (1)

m_L x + 1210 x = m_R y + m_o y

⇒ 1210 x = m_o y                  ...............(4) (using 3)

from (2) 

m_L + m_o x = m_R + 1000 y

⇒ m_o x = 1000 y                   ................(5) (using 3)

dividing equation (4) & (5) 

`"m"_"o"/1000 = 1210/"m"_"o"`

⇒ mO = `sqrt (1210 xx1000)` = 1100 g