Units and Dimensions

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

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

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

Which is different from others in units?

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

The equation $\left(p+\frac{a}{V^2}\right)(V-b)=$ constant. The unit of $a$ 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 value of surface tension of a niquia is 70 dyne/cm, then its value in $\mathrm{N} / \mathrm{m}$ will be

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

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…