Given Planck's constant ($h$), speed of light ($c$), and Newton's gravitational constant ($G$), determine the combination resulting in a quantity with dimensions of mass.

A new system of units uses force (F), velocity (V), and time (T) as fundamental units. What would be the unit of energy in this system?

The kinetic energy of a body is given by $K$. If the gravitational constant is represented by $G$, what are the dimensions of $\frac{K^2}{G}$?

If the unit of force is 100 N, unit of length is 10 m, and the unit of time is 100 s, what is the unit of mass in this system?

In the relation $y = a\cos \left( {\omega t - kx} \right)$, the dimensional formula for k is

$X = 3Y{Z^2}$ find dimension of Y in (MKS) system, If X and Z are the dimensions of capacity and magnetic field respectively

In the relation $P = \frac{\alpha }{\beta }{e^{\frac{{\alpha Z}}{{kheta }}}}$ P is pressure, Z is the distance, k is Boltzmann’s constant and $heta$ is the temperature. The dimensional formula of β will be

Given that $2l\sqrt {\frac{m}{T}}$, where l is the length of a string of linear density m, under tension T has the same dimensional formula as that of

Given Planck's constant ($h$), speed of light ($c$), and Newton's gravitational constant ($G$), determine the combination resulting in a quantity with dimensions of mass.

The frequency f of vibration of mass m suspended from a spring of spring constant k is given by $f = c{m^x}{k^y}$

Where c is dimensionless constant. The values of x and y are respectively

If force (F), velocity (V), and time (T) are taken as fundamental quantities, what are the dimensions of energy?