The value of gravitational acceleration in the $C.G.S.$ system is $980 \; cm/s^2$. Find the value of $g$ in the $M.K.S.$ system.

Convert $1 \; \text{newton}$ ($SI$ unit of force) into $dyne$ ($CGS$ unit of force).

$A$ force $F$ is given by $F = at + bt^2$,where $t$ is time. What are the dimensions of $a$ and $b$?

If the acceleration due to gravity is $10\,m/s^2$ and the units of length and time are changed to kilometer and hour respectively,the numerical value of the acceleration is

In the Van der Waals equation $\left[ P + \frac{a}{V^2} \right] [V - b] = RT$,where $P$ is pressure,$V$ is volume,$R$ is the universal gas constant,and $T$ is temperature,the ratio of constants $\frac{a}{b}$ is dimensionally equal to:

In an experiment,the percentage errors in the measurement of physical quantities $A, B, C,$ and $D$ are $1\%, 2\%, 3\%,$ and $4\%$ respectively. The maximum percentage error in the measurement of $X,$ where $X = \frac{A^2 B^{1/2}}{C^{1/3} D^3},$ will be: