The density of a material in the $CGS$ system of units is $4\,g/cm^3$. In a system of units in which the unit of length is $10\,cm$ and the unit of mass is $100\,g$,the value of the density of the material will be:

$(P+\frac{a}{V^2})(V-b)=RT$ represents the equation of state of some gases. Where $P$ is the pressure,$V$ is the volume,$T$ is the temperature and $a, b, R$ are the constants. The physical quantity,which has the same dimensional formula as that of $\frac{b^2}{a}$,will be

In the equation $(P+\frac{a}{V^2})(V-b)=RT$,where $P$ is pressure,$V$ is volume,$T$ is temperature,$R$ is universal gas constant,and $a$ and $b$ are constants. The dimensions of $a$ are

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:

Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful?

The time period of a body undergoing simple harmonic motion is given by $T=p^{a} D^{b} S^{c}$,where $p$ is the pressure,$D$ is density,and $S$ is surface tension. The values of $a, b,$ and $c$ respectively are