NEET Questions

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:

A student attempts to derive the formula for the period of a simple pendulum using dimensional analysis. They correctly identify the relevant variables as length (L), mass (m), and gravitational acceleration (g). Which of the following represents a fundamental limitation they will encounter?

Dimensional analysis is used to check the validity of an equation relating the speed of sound (v) in a gas to its pressure (P) and density ($\rho$). Which limitation prevents dimensional analysis from distinguishing between $v = \sqrt{P/\rho}$ and $v = \sqrt{14P/\rho}$?

A physicist uses dimensional analysis to derive an expression for the energy (E) of a particle based on its mass (m), velocity (v), and Planck's constant (h). They arrive at $E = mv^2$. Why is this result incomplete?

Which limitation of dimensional analysis prevents it from deriving the complete formula for the viscous force on a sphere moving through a fluid, given that the force (F) depends on the radius (r) of the sphere, its velocity (v), and the fluid's viscosity ($\eta$)?

A student uses dimensional analysis to analyze the time ($au$) it takes for a capacitor (C) to discharge through a resistor (R). They correctly identify that $au$ depends on R and C. However, they are unable to derive the precise relationship $au = RC$. What limitation of dimensional analysis explains this?