A uniform metre scale balances at 40 cm mark when weight of 20 and 40 g are suspended at 10 cm and 20 cm mark respectively. The mass of the metre scale is
(A)200g
(B)60g
(C)70g
(D)140g
Answers
Given info : A uniform metre scale balances at 40 cm mark when weight of 20 and 40 g are suspended at 10 cm and 20 cm mark respectively.
To find : the mass of the metre scale is...
solution : let mass of metre scale is m.
metre scale balances at 40cm mark so torque at 40cm mark must be equal to zero.
weight of metre scale acting vertically downward at centre of mass.
distance of balancing point from centre of mass of metre scale = 50cm - 40cm = 10cm
similarly, distance of mass 20g from balancing point = 10 - 40 = -30cm
distance of mass 40g from balancing point = 20 - 40 = -20cm
i.e., torque due to metre scale + torque due to mass of 20g + torque due to mass of 40g = 0
⇒mg × 10 + 20g × -30 + 40g × -20 = 0
⇒10m - 600 - 800 = 0
⇒m = 140g
Therefore the mass of metre scale is 140g