General Physics Question 21
Question 21
- $N$ divisions on the main scale of a vernier calipers coincide with $(N+1)$ divisions on the vernier scale. If each division on the main scale is of $a$ units, determine the least count of instrument.
$(2003,2 \mathrm{M})$
constant. The velocity $v$ of any point of the surface of the expanding sphere is proportional to
(2017 Adv.) (a) $R$ (b) $\frac{1}{R}$ (c) $R^{3}$ (d) $R^{\frac{2}{3}}$
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Answer:
Correct Answer: 22. $\frac{a}{N+1}$
Solution:
- $(N+1)$ divisions on the vernier scale
$$ =N \text { divisions on main scale } $$
$\therefore 1$ division on vernier scale
$$ =\frac{N}{N+1} \text { divisions on main scale } $$
Each division on the main scale is of $a$ units. $\therefore \quad 1$ division on vernier scale $=\frac{N}{N+1} \quad a$ units $=a^{\prime}$ (say)
Least count $=1$ main scale division -1 vernier scale division
$$ =a-a^{\prime}=a-\frac{N}{N+1} \quad a=\frac{a}{N+1} $$
