JEE Main · 2009 · 12 Apr 2009 · Offline · Units & Measurement

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In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (

= 0. 5^{\circ}

), then the least count of the instrument is

(A)one minute✓ Correct
(B)half minute
(C)one degree
(D)half degree

Answer: (A)

Solution

Each vernier division is a little shorter than a main-scale division, and the least count is exactly that difference. Since 29 main-scale divisions coincide with 30 vernier divisions, one vernier division equals

\frac{29}{30}

of a main-scale division, so the smallest length the instrument can resolve is

\frac{1}{30}

of a main-scale division. With each main-scale division worth half a degree, this is

\frac{1}{30} \times \frac{1}{2}^{\circ} = \frac{1}{60}^{\circ}

, and because one degree contains sixty minutes of arc, the least count works out to one minute.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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JEE Main · 2009 · 12 Apr 2009 · Offline · Units & Measurement

Solution

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