The dimensions of physical quantity $X$ in the equation $\text{Force} = \frac{X}{\text{Density}}$ are given by:

If the units of force,energy,and velocity are respectively $10\, N$,$100\, J$,and $5\, m/s$,then the units of length,mass,and time will be:

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A\sqrt{x}}{x + B}$, where $A$ and $B$ are constants with appropriate dimensions. The dimensions of $AB$ are . . . . . . .

The equation of a stationary wave is given by $y = 2a \sin \left( \frac{2 \pi nt}{\lambda} \right) \cos \left( \frac{2 \pi x}{\lambda} \right)$. Which of the following statements is $NOT$ correct?

$A$ neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$,where $\mu_{0}$ and $c$ are the permeability and speed of light in free space,respectively. Then,

If velocity $[V]$,time $[T]$,and force $[F]$ are chosen as the base quantities,the dimensions of mass will be: