A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:
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,
The dimensions of $K$ in the equation $W = \frac{1}{2}\,\,K{x^2}$ is
If speed $V,$ area $A$ and force $F$ are chosen as fundamental units, then the dimension of Young's modulus will be :