The speed of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be

The force $F$ on a sphere of radius $a$ moving in a medium with velocity $v$ is given by $F = 6\pi \eta av$. The dimensions of $\eta$ are

If the relationship between velocity,acceleration,and force in two systems is given by $v_2 = \frac{\alpha^2}{\beta} v_1$,$a_2 = \alpha \beta a_1$,and $F_2 = \frac{F_1}{\alpha \beta}$,then what is the relationship between mass,length,and time?

$A$ wave pulse can travel along a tense string like a violin string. $A$ series of experiments showed that the wave velocity $V$ of a pulse depends on the following quantities: the tension $T$ of the string,the cross-sectional area $A$ of the string,and the density $\rho$ (mass per unit volume) of the string. Obtain an expression for $V$ in terms of $T$,$A$,and $\rho$ using dimensional analysis.

If energy $(E)$,velocity $(V)$,and time $(T)$ are chosen as the fundamental quantities,the dimensional formula of surface tension will be

If energy $(E)$,velocity $(v)$,and force $(F)$ are taken as fundamental quantities,what are the dimensions of mass?