Linear and Angular Measurement Questions and Answers

Answer: D

A micrometer works on the principle of the nut and bolt, that is, a screw turning in a nut.

The spindle carries a precision screw thread, usually of 0.5 mm pitch, that turns in a fixed nut in the frame. Each full turn of the thimble moves the spindle along its axis by exactly one pitch, so a small linear movement is magnified into a large, easily divided rotation: one of 50 thimble divisions is 0.01 mm.

'Screw' alone names only half of the pair; the principle depends on the screw moving in a nut. A bolt alone or a stud cannot convert rotation into a measured advance.

Answer: A

The correct reading is found by adding the negative error to the actual reading.

A negative zero error means that with the measuring faces closed, the zero of the thimble has gone past the datum line, so the micrometer reads less than the true size. Every reading is too small by the size of the error, so the magnitude of the error must be added back: true size = observed reading + error.

Deducting it would make the reading smaller still. The 'twice the error' options have no basis, since the error is a fixed offset that applies once to each reading.

Answer: B

The least count is 0.05 mm.

Least count is one main scale division minus one vernier scale division. Here 20 vernier divisions span 19 mm, so one vernier division is \(19/20 = 0.95\) mm:

\[ \begin{aligned} \text{LC} &= 1\ \text{mm} - 0.95\ \text{mm} \\ &= 0.05\ \text{mm} \end{aligned} \]

Equivalently, LC is one main scale division divided by the number of vernier divisions, \(1/20\). 0.02 mm would need 50 vernier divisions over 49 mm, and 0.01 mm is the least count of a standard micrometer.

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.