The Young's modulus of a wire is given by $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $L$ is length,$A$ is cross-sectional area,and $\Delta L$ is the change in length. By what factor must we multiply to convert the value from $CGS$ units to $MKS$ units?

In the expression $A=B+\frac{C}{D+E}$,the dimensions of physical quantities $B$ and $C$ are $[L^{1} M^{0} T^{-1}]$ and $[L^{1} M^{0} T^{0}]$ respectively. The dimensions of quantities $A, D$ and $E$ are

Which of the following relations cannot be deduced using dimensional analysis? [the symbols have their usual meanings]

$E, m, L, G$ represent energy,mass,angular momentum,and gravitational constant respectively. The dimensions of $\frac{EL^2}{m^5 G^2}$ will be that of

If the time period $t$ of the oscillation of a drop of liquid of density $d$,radius $r$,vibrating under surface tension $s$ is given by the formula $t = \sqrt{r^{2b} s^c d^{a/2}}$. It is observed that the time period is directly proportional to $\sqrt{\frac{d}{s}}$. The value of $b$ should therefore be

The velocity of a freely falling body changes as ${g^p}{h^q}$ where $g$ is the acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ are: