Dimensions & Dimensional Formulae — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Dimensions & Dimensional Formulae MCQs with step-by-step solutions (21 questions). Part of Units and Measurements (Std 11). Practise online on Prepizo — no login needed.
▶ Practise Dimensions & Dimensional Formulae online (free)
Questions with solutions
Q1 — Dimensions & Dimensional Formulae · easy · theory
The dimensional formula of a physical quantity expresses:
A. The unit in which the quantity is measured
B. The numerical value of the quantity
C. The accuracy of the measurement
D. How the quantity depends on the fundamental quantities ✓ Correct
Solution: It is written using the symbols $M$, $L$, $T$, $A$, $K$, $\text{mol}$ and $\text{cd}$.
Q2 — Dimensions & Dimensional Formulae · easy · theory
Which of the following is a dimensionless quantity?
A. Force
B. Pressure
C. Momentum
D. Strain ✓ Correct
Solution: Strain is a ratio of two lengths, so the dimensions cancel. Angle and refractive index are likewise dimensionless.
Q3 — Dimensions & Dimensional Formulae · easy · theory
The dimensional formula of force is:
A. $[M^1L^1T^{-2}]$ ✓ Correct
B. $[M^1L^{-1}T^{-2}]$
C. $[M^1L^1T^{-1}]$
D. $[M^1L^2T^{-2}]$
Solution: From $F = ma$: $[M][LT^{-2}] = [M^1L^1T^{-2}]$.
Q4 — Dimensions & Dimensional Formulae · easy · theory
The dimensional formula of work and of energy is:
A. $[M^1L^2T^{-2}]$ ✓ Correct
B. $[M^1L^1T^{-2}]$
C. $[M^1L^2T^{-1}]$
D. $[M^1L^2T^{-3}]$
Solution: Work is force times distance, so $[M^1L^1T^{-2}][L] = [M^1L^2T^{-2}]$.
Q5 — Dimensions & Dimensional Formulae · medium · theory
The dimensional formula of power is:
A. $[M^1L^1T^{-3}]$
B. $[M^1L^2T^{-2}]$
C. $[M^1L^2T^{-1}]$
D. $[M^1L^2T^{-3}]$ ✓ Correct
Solution: Power is work per unit time, so one more power of $T$ appears in the denominator.
Q6 — Dimensions & Dimensional Formulae · medium · theory
The dimensional formula of pressure is:
A. $[M^1L^{-1}T^{-2}]$ ✓ Correct
B. $[M^1L^{-2}T^{-2}]$
C. $[M^1L^2T^{-2}]$
D. $[M^1L^1T^{-2}]$
Solution: Pressure is force per unit area: $\dfrac{[M^1L^1T^{-2}]}{[L^2]}$.
Q7 — Dimensions & Dimensional Formulae · medium · theory
Two physical quantities having the same dimensional formula:
A. Must always be the same quantity
B. Must both be dimensionless
C. May be different quantities, such as work and torque ✓ Correct
D. Cannot be added together
Solution: Dimensional identity does not imply physical identity — work and torque are a standard example.
Q8 — Dimensions & Dimensional Formulae · medium · theory
A dimensional constant is one that:
A. Changes value from place to place
B. Has no dimensions, such as $\pi$
C. Has a fixed value and also possesses dimensions, such as $G$ or $h$ ✓ Correct
D. Has dimensions but no fixed value
Solution: Pure numbers like $\pi$ and $e$ are dimensionless constants by contrast.
Q9 — Dimensions & Dimensional Formulae · easy · theory
The dimensional formula of linear momentum is:
A. $[M^1L^2T^{-1}]$
B. $[M^1L^1T^{-1}]$ ✓ Correct
C. $[M^1L^2T^{-2}]$
D. $[M^1L^1T^{-2}]$
Solution: Momentum is mass times velocity.
Q10 — Dimensions & Dimensional Formulae · medium · numerical
Which of the following pairs has identical dimensional formulae?
A. Work and torque ✓ Correct
B. Momentum and energy
C. Force and pressure
D. Power and force
Solution: Both work and torque have $[M^1L^2T^{-2}]$, since torque is $\vec{r} \times \vec{F}$.
Q11 — Dimensions & Dimensional Formulae · hard · numerical
The dimensional formula of the universal gravitational constant $G$ is:
A. $[M^{-1}L^2T^{-2}]$
B. $[M^{-1}L^3T^{-2}]$ ✓ Correct
C. $[M^1L^3T^{-2}]$
D. $[M^{-2}L^3T^{-1}]$
Solution: From $F = \dfrac{Gm_1m_2}{r^2}$, $G = \dfrac{Fr^2}{m^2}$, giving $[M^{-1}L^3T^{-2}]$.
Q12 — Dimensions & Dimensional Formulae · hard · numerical
In the equation of state $\left(P + \dfrac{a}{V^2}\right)(V - b) = RT$, the dimensional formula of $a$ is:
A. $[M^1L^5T^{-2}]$ ✓ Correct
B. $[M^1L^{-1}T^{-2}]$
C. $[M^0L^3T^0]$
D. $[M^1L^3T^{-2}]$
Solution: $\dfrac{a}{V^2}$ must have the dimensions of pressure, so $[a] = [M^1L^{-1}T^{-2}][L^6] = [M^1L^5T^{-2}]$.
Q13 — Dimensions & Dimensional Formulae · hard · numerical
If a force is given by $F = at + bt^2$ where $t$ is time, the dimensional formula of $b$ is:
A. $[M^1L^1T^{-4}]$ ✓ Correct
B. $[M^1L^1T^{-2}]$
C. $[M^1L^1T^{-3}]$
D. $[M^1L^1T^{-1}]$
Solution: By homogeneity $[b][T^2] = [M^1L^1T^{-2}]$, so $[b] = [M^1L^1T^{-4}]$.
Q14 — Dimensions & Dimensional Formulae · hard · numerical
The dimensional formula of Planck's constant is:
A. $[M^1L^2T^{-1}]$ ✓ Correct
B. $[M^1L^2T^{-3}]$
C. $[M^1L^2T^{-2}]$
D. $[M^1L^1T^{-1}]$
Solution: From $E = h\nu$, $[h] = \dfrac{[M^1L^2T^{-2}]}{[T^{-1}]} = [M^1L^2T^{-1}]$.
Q15 — Dimensions & Dimensional Formulae · medium · numerical
The dimensional formula of angular momentum is:
A. $[M^1L^2T^{-3}]$
B. $[M^1L^2T^{-1}]$ ✓ Correct
C. $[M^1L^1T^{-1}]$
D. $[M^1L^2T^{-2}]$
Solution: $L = mvr$ gives $[M][LT^{-1}][L] = [M^1L^2T^{-1}]$ — the same as Planck's constant.
Q16 — Dimensions & Dimensional Formulae · hard · numerical
The dimensional formula of the coefficient of viscosity is:
A. $[M^1L^{-2}T^{-1}]$
B. $[M^1L^1T^{-1}]$
C. $[M^1L^{-1}T^{-2}]$
D. $[M^1L^{-1}T^{-1}]$ ✓ Correct
Solution: From $F = \eta A\dfrac{dv}{dx}$, $[\eta] = \dfrac{[M^1L^1T^{-2}]}{[L^2][T^{-1}]} = [M^1L^{-1}T^{-1}]$.
Q17 — Dimensions & Dimensional Formulae · medium · numerical
The dimensional formula of surface tension is:
A. $[M^1L^0T^{-2}]$ ✓ Correct
B. $[M^1L^2T^{-2}]$
C. $[M^1L^1T^{-2}]$
D. $[M^1L^{-1}T^{-2}]$
Solution: Surface tension is force per unit length: $\dfrac{[M^1L^1T^{-2}]}{[L]}$.
Q18 — Dimensions & Dimensional Formulae · hard · numerical
The dimensional formula of magnetic flux is:
A. $[M^0L^2T^{-2}A^{-1}]$
B. $[M^1L^1T^{-2}A^{-1}]$
C. $[M^1L^2T^{-2}A^{-1}]$ ✓ Correct
D. $[M^1L^2T^{-1}A^{-2}]$
Solution: $\Phi = BA$ with $B = \dfrac{F}{IL}$ gives $[M^1L^2T^{-2}A^{-1}]$.
Q19 — Dimensions & Dimensional Formulae · medium · numerical
The dimensional formula of impulse is the same as that of:
A. Force
B. Energy
C. Momentum ✓ Correct
D. Power
Solution: Impulse is force times time, $[M^1L^1T^{-1}]$, which is exactly the dimension of momentum.
Q20 — Dimensions & Dimensional Formulae · easy · numerical
The dimensional formula of frequency is:
A. $[M^0L^0T^1]$
B. $[M^0L^0T^{-1}]$ ✓ Correct
C. $[M^1L^0T^{-1}]$
D. $[M^0L^1T^{-1}]$
Solution: Frequency is the number of cycles per second, so only time appears.
Q21 — Dimensions & Dimensional Formulae · hard · numerical
The dimensional formula of gravitational potential is:
A. $[M^0L^1T^{-2}]$
B. $[M^1L^{-1}T^{-2}]$
C. $[M^0L^2T^{-2}]$ ✓ Correct
D. $[M^1L^2T^{-2}]$
Solution: Gravitational potential is potential energy per unit mass: $\dfrac{[M^1L^2T^{-2}]}{[M]}$.