Measurement of Length and Motion: 18 MCQs with answers

The metre

The metre ($m$) is the SI base unit of length; centimetre, kilometre and millimetre are derived units built from it by powers of ten.

Parallax error

Parallax error occurs when the eye is not directly above the reading mark, so the reading appears shifted.

In motion

Rest and motion are relative. The passenger is at rest relative to the train but in motion relative to the platform.

Periodic motion

Periodic motion repeats at fixed time intervals, which is exactly what a swinging pendulum does.

Distance

Distance is a scalar — it has magnitude only. Displacement and velocity are vectors because they include direction.

Dust particles floating in a sunbeam

Random motion has no predictable path, like dust particles in a sunbeam. The others are rectilinear, circular and periodic respectively.

True

The metre is defined as the distance light travels in vacuum in $\frac{1}{299,792,458}$ of a second, making it a universal and unchanging standard.

Distance is the lap length; displacement is zero

Distance is the total path length (one lap), but displacement is the straight-line change in position, which is zero because start and finish coincide.

$10\text{ m/s}$

Multiply km/h by $\frac{5}{18}$: $36 \times \frac{5}{18} = 10\text{ m/s}$.

Velocity should use displacement, not distance

Velocity is displacement divided by time. Using distance gives speed, not velocity, because direction is missing.

The speed of light is a universal constant that never changes

A metal bar expands with heat and can be damaged, so it is not truly fixed. The speed of light in vacuum is a constant of nature, making the definition universal and unchanging.

The least count uncertainty of the instrument

The $\pm$ value is the least count uncertainty — the smallest change the instrument can reliably detect. Every measurement carries some uncertainty.

Mixing units like km and seconds gives a meaningless result

If distance is in kilometres and time in seconds, the result is a mix of units that has no physical meaning. Always convert to consistent units first.

Its velocity changes because its direction keeps changing

Velocity is a vector. Even at constant speed, a change in direction means the velocity changes — this is why circular motion at constant speed still has changing velocity.

Average speed $= 60\text{ km/h}$; average velocity $= 0\text{ km/h}$

Average speed uses total distance ($120\text{ km}$) over total time ($2\text{ h}$) $= 60\text{ km/h}$. Average velocity uses net displacement, which is zero for a round trip, so it is $0\text{ km/h}$.

$7.8\text{ cm}$

The object's end must align with the zero mark, not the ruler's edge. Since the edge is $2\text{ mm}$ ($0.2\text{ cm}$) before zero, the reading is too large by $0.2\text{ cm}$: $8.0 - 0.2 = 7.8\text{ cm}$.

8.25 m/s

To find the average speed, first convert the time from minutes to seconds: $3 \text{ minutes} = 180 \text{ seconds}$. Then use the formula for speed: $v = \frac{d}{t} = \frac{1498.5 \text{ m}}{180 \text{ s}} \approx 8.25 \text{ m/s}$.

0.5 m/s; because average speed only considers distance

The average velocity is calculated as the net displacement over time. For one complete lap, the displacement is 0 m (the runner returns to the starting point), so average velocity is $\frac{0 \text{ m}}{120 \text{ s}} = 0 \text{ m/s}$. The average speed, however, is the total distance (circumference…