A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x×10−2 kg. The value of x is
Answer: 6
Solution
Let the mass of the metre scale be m. Initially, the scale balances at its center (50 cm mark). When coins are added at 10 cm and the new balance point is at 40 cm, we apply the principle of moments.
Taking torques about the knife edge at 40 cm:
The two coins (total mass = 20 g = 0.02 kg) are at distance (40−10)=30 cm from the knife edge.
The center of mass of the scale (at 50 cm) is at distance (50−40)=10 cm from the knife edge.
For equilibrium:
(0.02 kg)×g×(30×10−2 m)=m×g×(10×10−2 m)
0.02×30=m×10
m=100.6=0.06 kg=6×10−2 kg
Therefore, x=6.
JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Integer answer
