The unit of the ratio between thrust and impulse is same as that of
- (a)frequency
- (b)speed
- (c)wavelength
- (d)acceleration
Correct — A, frequency. Thrust is a force, so its SI unit is the newton (N = kg·m/s²). Impulse is force multiplied by the time for which it acts, so its unit is the newton-second (N·s). The ratio thrust ÷ impulse = N ÷ (N·s) = 1/s = s⁻¹. That is exactly the unit of frequency, the hertz (Hz = s⁻¹). So the ratio has the same unit — and dimension (T⁻¹) — as frequency.
- (b)speed — Speed has the unit metre per second (m/s), dimension L·T⁻¹, which is different from s⁻¹.
- (c)wavelength — Wavelength is a length, measured in metres (m), dimension L — nothing like a per-second unit.
- (d)acceleration — Acceleration has the unit metre per second squared (m/s²), dimension L·T⁻², not the required s⁻¹.
This is a dimensional-analysis question. Thrust is a force (unit newton). Impulse equals force times time (unit newton-second), and it also equals the change in momentum. Dividing thrust by impulse cancels the force and leaves the reciprocal of time, whose unit s⁻¹ is that of frequency.
The quick route is to write each quantity's unit and simplify: N ÷ (N·s) = 1/s. Recognising that 'per second' is the signature of frequency (Hz) gives the answer without any numbers. The distractors are common mechanical quantities whose units are metre-based, so they cannot match a pure per-second unit.
- Thrust is a force; its unit is the newton (N).
- Impulse = force × time; its unit is the newton-second (N·s).
- Thrust ÷ impulse = N/(N·s) = s⁻¹, dimension T⁻¹.
- Frequency is measured in hertz (Hz = s⁻¹) — the same unit.
- Confusing impulse (N·s) with force (N) and cancelling incorrectly.
- Overlooking that a pure 'per second' unit points to frequency, not a metre-based quantity.
Asked as a dimensional-analysis match: reduce the unit of a ratio of quantities and identify which listed quantity shares it.
No directly related past PYQ was found.
- practice — not a real PYQ
The SI unit of impulse is the same as that of
- (a)force
- (b)momentum
- (c)energy
- (d)power
Answer(b) momentum — impulse equals the change in momentum, so both have the unit kg·m/s (N·s).
- practice — not a real PYQ
Which one of the following has the same dimensional formula as frequency?
- (a)Angular velocity
- (b)Velocity
- (c)Acceleration
- (d)Wavelength
Answer(a) Angular velocity — both frequency and angular velocity have the dimension T⁻¹ (per second).