Q 11-06-129JEE MainJEE Main 2022 (24 Jun, Shift 1)Easy
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass $10\ \text{g}$, are put one on top of the other at the $10.0\ \text{cm}$ mark, the scale is found to be balanced at the $40.0\ \text{cm}$ mark. The mass of the metre scale is found to be $x\times10^{-2}\ \text{kg}$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 6
The scale's weight acts at its centre (50 cm mark). Taking moments about the new pivot at 40 cm:
$$20\ \text{g}\times(40-10) = M\times(50-40)\ \Rightarrow\ M = 60\ \text{g} = 6\times10^{-2}\ \text{kg}$$
So $x = 6$.
Solution by Sreeraj P, M.Sc Physics