Units and Dimensions

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

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…

Planck's constant (h), speed of light in a vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

If dimensions of critical velocity, vc of a liquid flowing through a tube are expressed as $\eta$x$\rho$yrz, where, $\eta$, $\rho$ and r are the coefficient of viscosity of liquid, density of liquid and radius of the…

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 &…

Match List - I with List - II : List - I List - II (a) Gravitational constant (G) (i) \$[L^{2}T^{-2}]$ (b) Gravitational potential energy (ii) \$[M^{-1}L^{3}T^{-2}]$ (c) Gravitational potential (iii) \$[LT^{-2}]$ (d)…

If force F, velocity V and time T are taken as fundamental units, the dimensions of mass are

Consider that $\sigma_s$, $k_B$, b represent Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_s k_B^{-1}b$ is :

Each side of a metallic cube of mass $5.580$ kg is measured to be $9.0$ cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as $X \times 10^{3}$ kg m$^{-3}$, where…

The speed of light in vacuum is taken as unity. If light takes $6$ min $40$ s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is :