Q 11-01-160JEE MainJEE Main 2022 (26 Jul, Shift 1)Medium
A screw gauge of pitch $0.5\ \text{mm}$ is used to measure the diameter of a uniform wire of length $6.8\ \text{cm}$. The main scale reading is $1.5\ \text{mm}$ and the circular scale reading is $7$. The calculated curved surface area of the wire to appropriate significant figures is [Screw gauge has $50$ divisions on the circular scale]
Answer: (B) $3.4\ \text{cm}^2$
Least count $= \dfrac{0.5}{50} = 0.01\ \text{mm}$. Diameter $d = 1.5 + 7\times0.01 = 1.57\ \text{mm} = 0.157\ \text{cm}$.
$$A = \pi dl = 3.14\times0.157\times6.8\approx3.35\ \text{cm}^2$$
The length $6.8\ \text{cm}$ has two significant figures, so $A\approx3.4\ \text{cm}^2$.
Solution by Sreeraj P, M.Sc Physics