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

The square root of the product of inductance and capacitance has the dimension of

Match List - I with List - II : List - I List - II (a) Gravitationalconstant (G) (i) $\left[L^{2}T^{-2}\right]$ (b) Gravitationalpotential energy (ii) $\left[M^{-1}L^{3}T^{-2}\right]$ (c) Gravitationalpotential (iii)…

A physical quantity of the dimensions of length that can be formed out of $c,G$ and $\frac{e^{2}}{4\pi\,\epsilon\,_{0}}$,where [$c$ is velocity of light, $G$ is universal constant of gravitation,$e$ is charge…

Plane angle and solid angle have:

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:

Match the following:

Match the List-I with List-II. The correct match in the following is

The dimensional formula of Planck's constant is

If the equation for the velocity of a particle at time ' $t$ ' is $v=a t+\frac{b}{t+c}$, then the dimensions of $a, b, c$ are respectively

Of the following, the pair of physical quantities not having the same dimensional formula is