NEET Physics Units And Measurement Dimensional Analysis MCQs

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv$. If a new physical quantity $Q$ is defined as $Q = \frac{Fv^2}{\eta^2 r^3}$, the dimensions of $Q$ are:

The speed of sound in a medium depends on the modulus of elasticity $E$ and density $\rho$ of the medium. Using dimensional analysis, determine the relationship between these quantities.

The energy of a photon is given by $E = h

u$, where$h$is Planck's constant and$

u$is the frequency. If a new quantity$X$is defined as$X = \frac{h^2

u^3}{E}$, the dimensions of$X$ are:

Given the expression for the escape velocity $v_e = \sqrt{\frac{2GM}{R}}$, where $G$ is the gravitational constant, $M$ is mass, and $R$ is radius. If a new quantity $Y$ is defined as $Y = \frac{v_e^3}{\sqrt{GM}}$, what are the dimensions of $Y$?

The wavelength $\lambda$ of matter waves is given by $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is momentum. If a new quantity $Z$ is defined as $Z = \frac{h^2}{\lambda^2 p c}$, where $c$ is the speed of light, the dimensions of $Z$ are:

Which of the following is a dimensionless quantity?

Which of the following has the dimensions of $ML^{-1}T^{-2}$?

The dimensions of gravitational constant G are:

If the dimensions of a physical quantity are $ML^2T^{-2}$, what could it represent?

Which pair of quantities have the same dimensions?