What is the mass of the metre stick?

A metre stick is balanced on a knife-edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick?

Solutions

Expert Solution

The centre of mass of the meter rule shifts to 45 cm mark from 50 cm mark when 2 coins are added at 12 cm mark.

Mass of two coins, m = 10 g

Distance at which the coins are placed from the new support d1= 45 – 12 = 33 cm

Distance of the centre of mass from the new support= 50- 45 = 5 cm

To find the mass of the scale, we should use the balancing moments

Moment due to the coins, r1 = m x d1

Moment due to the mass of the scale r2 = M x d2

r1 = r2

m x d1 = M x d2

Substituting we get

10 x 33 = M x d2

M = (10 x 33) /5 = 330/5 = 66 g

The mass of the metre stick is 66 g.

Ajay Kumar Gupta answered 2 years ago

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