If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then
$a = 1/3,\,b = 1/3,\,c = - 1/3$
$a = 1/2,\,b = 1/2,\,c = - 1/2$
$a = 1/2,\,b = - 1/2,\,c = 1/2$
$a = 1/2,\,b = - 1/2,\,c = - 1/2$
Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful
If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is
A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^7 c^5$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by
The equation of a wave is given by$Y = A\sin \omega \left( {\frac{x}{v} - k} \right)$where $\omega $ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is
In terms of basic units of mass $(M)$, length $(L)$, time $(T)$ and charge $(Q)$, the dimensions of magnetic permeability of vacuum $\left(\mu_0\right)$ would be