Units and Dimensions

If the errors involved in the measurement of a side and the mass of a cube are $2\%$ and $4\%$ respectively, the maximum permissible error in the density of the material is

If the mass of the object is measured as $m = (7 \mp 0.14)$ kg and the density is measured as $\rho = (5 \mp 0.25)$ kg/m$^3$ respectively. The percentage error in the measurement of volume is

Which is different from others in units?

Number of particles is given by $n=-D \frac{n_2-n_1}{x_2-x_1}$ crossing a unit area perpendicular to $X$-axis is unit time, where $n_1$ and $n_2$ are number of particles per unit volume for the value of $x$ meant to…

- If $L, C$ and $R$ denote the inductance, capacitance and resistance respectively, the dimensional formula for $C^2 L R$ is

The displacement of an oscillating particle is given by $y=A \sin [B x+C t+D t]$. The dimensional formula for $[A B C D]$ is :

If force is proportional to square of velocity, then the dimensions of proportionality constant is

Position of a body with acceleration $a$ is given by $x=k a^m t^n$, here $t$ is time, find the dimension of $m$ and $n$

If value of surface tension of a niquia is 70 dyne/cm, then its value in $\mathrm{N} / \mathrm{m}$ will be

The equation $\left(p+\frac{a}{V^2}\right)(V-b)=$ constant. The unit of $a$ is

If $E=$ energy, $G=$ gravitational constant, $I=$ impulse and $M=$ mass, then dimensions of $\frac{G I M^2}{E^2}$ are same as that of

If force is proportional to square of velocity, then the dimensions of proportionality constant is