calculate the mass

Question

A uniform meter rule of mass 90g is pivoted at the 40cm mark. If the rule is in equilibrium with an unknown mass M placed at the 10cm mark and a 72g mass at the 70cm mark, determine M

Answer 1

Assume all of the mass of the meter ruler is centered at center of gravity at 50 cm.

 

Sum of the torques must be zero

 

Pivot is at 40 cm

Torque due to mass of ruler = 10 * 90 = 900 g cm

Torque due to 72 g = 30 * 72 = 2160 g cm

Torque due to M = M * 30 and opposite direction

 

30 M = 2160 + 900 = 3060

 

M = 102 g