Discussion
The least count of a 200 mm long spirit level is given as 10 sec per division. The gradient of the spirit level expressed as mm over one meter is:
Answer: A
The gradient is 0.048 mm per metre.
One division of the level corresponds to a tilt of 10 seconds of arc. Convert that to radians and multiply by 1 m (1000 mm):
\[ \begin{aligned} 10'' &= \frac{10}{3600} \times \frac{\pi}{180} = 4.85 \times 10^{-5}\ \text{rad} \\ \text{rise} &= 1000 \times 4.85 \times 10^{-5} \\ &= 0.048\ \text{mm} \end{aligned} \]
For angles this small, the tangent equals the angle in radians. The 200 mm length of the level does not affect the answer, since the gradient is asked over one metre. 0.48 mm is ten times too large, and 1.048 mm and −1.048 mm add a stray 1.
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