List of top Physics Questions on Dimensional Analysis

If the velocity of light $c$, universal gravitational constant $G$ and Planck's constant $h$ are chosen as fundamental quantities The dimensions of mass in the new system is :

Identify the pair of physical quantities which have different dimensions.

Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Time period of oscillation of a liquid drop depends on surf ace tension (S), if density of the liquid is ρ and radius of the drop is r, then $T=K\sqrt {\frac {ρr^3}{S^{\frac 32}}}$ is dimensionally correct, where K is dimensionless.
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as
$v_2=\frac{n}{m^2}v_1$ and $a_2=\frac{a_1}{mn}$
respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 10² Hz

If force $[ F ]$, acceleration $[ A ]$ and time $[ T ]$ are chosen as the fundamental physical quantities. Find the dimensions of energy.

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

The dimension of stopping potential $V_0$ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :

The dimensional formula for permittivity of free space $\left(\left(\epsilon \right)_{0}\right)$ in the equation $F=\frac{1}{4 \pi \epsilon _{0}}\frac{q_{1} q_{2}}{r^{2}}$ , where symbols have their usual meaning, is

The dimensional formula for entropy is

If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be : -

What is the dimension of energy in terms of linear momentum (P), area (A) and time (T).

If mass (M), distance (L) and time (T) are the fundamental quantities then dimension of torque is

The dimensional formula of coefficient of viscosity can be expressed as $ M^a\, L^bT^c $ . What are the values of $ a $ , $ b $ and $ c $ .

The dimensions of torque are same as that of

The dimensional formula of Reynold?? number is same as

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $G, h$ and $c$. Which of the following correctly gives the Planck length ?