Question

A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

Answer 1

Answer:

126.99115 g

Explanation:

50 g at 90 cm

Stick balances at 61.3 cm

x = Distance of the third 0.6 kg mass

Meter stick hanging at 50 cm

Torque about the support point is given by (torque is conserved)

$mgl_1=Mgl_2\\\Rightarrow M=\dfrac{ml_1}{l_2}\\\Rightarrow M=\dfrac{50\times (61.3-90)}{50-61.3}\\\Rightarrow M=126.99115\ g$

The mass of the meter stick is 126.99115 g

Answer 2

Answer:

127 g

Explanation:

Let m be the mass of the metre stick.

50 g mass is placed on 90 cm mark is balance at 61.3 cm mark. Take moments about the 61.3 cm mark.

Anticlockwise torque = clock wise torque

m x (61.3 - 50) = 50 x (90 - 61.3)

m x 11.3 = 50 x 28.7

m = 127 g

Thus, the mass of the mere stick is 127 g.