Units and Dimensions

Plane angle and solid angle have:

Match List - I with List - II : List - I List - II (a) Gravitationalconstant (G) (i) $\left[L^{2}T^{-2}\right]$ (b) Gravitationalpotential energy (ii) $\left[M^{-1}L^{3}T^{-2}\right]$ (c) Gravitationalpotential (iii)…

A physical quantity of the dimensions of length that can be formed out of $c,G$ and $\frac{e^{2}}{4\pi\,\epsilon\,_{0}}$,where [$c$ is velocity of light, $G$ is universal constant of gravitation,$e$ is charge…

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

Match List I with List II. List I List II (A) Torque (I) $\mathrm{Nms}^{-1}$ (B) Stress (II) $\mathrm{Jkg}^{-1}$ (C) Latent Heat (III) $\mathrm{Nm}$ (D) Power (IV) $\mathrm{Nm}^{-2}$ Choose the correct answer from the…

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right]$. If $b=-3$, the value of $c$ is ________

Match List I with List II List I List II A Angular momentum I $\left[\mathrm{ML}^{2}T^{-2}\right]$ B Torque II $\left[\mathrm{ML}^{-2}T^{-2}\right]$ C Stress III $\left[\mathrm{ML}^{2}T^{-1}\right]$ D Pressure gradient…

A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t=A \rho^{a} r^{b} \eta^{\mathrm{c}} \sigma^{d}$,…

Match List - I with List - II. List - I List - II a Torque i $\mathrm{MLT}^{-1}$ b Impulse ii $\mathrm{MT}^{-2}$ c Tension iii $\mathrm{ML}^{2}T^{-2}$ d Surface Tension iv $\mathrm{MLT}^{-2}$ Choose the most appropriate…

Match List - I with List - II : List - I List - II a Magnetic induction i $\mathrm{ML}^{2}T^{-2}A^{-1}$ b Magnetic flux ii $M^{0}L^{-1}A$ c Magnetic permeability iii $\mathrm{MT}^{-2}A^{-1}$ d Magnetization iv…

The force is given in terms of time $t$and displacement $x$ by the equation $F=A\cos\,Bx+C\sin\,Dt$ The dimensional formula of $\frac{AD}{B}$ is:

Assertion A: Product of Pressure $\left(P\right)$and time $\left(t\right)$ has the same dimension as that of coefficient of viscosity. Reason: Coefficient of viscosity…