JEE Main · 2012 · 29 Apr 2012 · Offline · Units & Measurement

WhatsApp Email

A spectrometer gives the following reading when used to measure the angle of a prism.

Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

(A) $58.5 9^{\circ}$
(B) $58.7 7^{\circ}$
(C) $58.6 5^{\circ}$ ✓ Correct
(D) $5 9^{\circ}$

Answer: (C)

Solution

The least count is one main-scale division minus one vernier division. Since

30

vernier divisions span

29

main divisions, one vernier division is

\frac{29}{30}

of a main division, so the least count is

0. 5^{\circ} (1 - \frac{29}{30}) = \frac{0. 5 ^{\circ}}{30} = \frac{1}{60}^{\circ}

. The reading is the main-scale value plus the vernier count times the least count:

58. 5^{\circ} + 9 \times \frac{1}{60}^{\circ} = 58. 5^{\circ} + 0.1 5^{\circ} = 58.6 5^{\circ}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

Practise more: all JEE Main PYQs on Units & Measurement →

JEE Main · 2012 · 29 Apr 2012 · Offline · Units & Measurement

Solution

More JEE Main questions on Units & Measurement