Units & measurements practice · Hard

In gas equation $\left( {P + \frac{a}{{{V^2}}}} \right)\left( {V - b} \right) = RT$, where T is absolute temperature, P is the pressure and V is the volume of the gas. The dimensional formula of $\left( {\frac{a}{{{V^2}}}} \right)$ is

The reverberation period T of a room depends on its volume V, its surface area A and velocity of sound C. If K is dimensionless constant then T =

If the error in the measurement of the volume of a sphere is 4.5%, then error in the measurement of its surface area is

A gas bubble from an explosion under water oscillates with a time period T, depends upon static pressure p, density of water $\rho$ and the total energy of explosion E. Find the expression for the time period T.(where, k is a dimensionless constant)

If K denotes coefficient of thermal conductivity, d the density and c the specific heat, the unit of X, where X=K/dc will be

The focal length of a mirror is given by $\frac{1}{f} = \frac{1}{u} + \frac{{1\;}}{v}$ where u and $v$ represent object and image distances respectively. The maximum relative error in $f$ is

A student performs an experiment for determination of $\mathrm{g}\left( { = \frac{{4{\mathrm{\pi }^2}l}}{{{T^2}}}} \right),\mathrm{\;}l \approx 1\mathrm{m},$, and he commits an error of $\Delta l.$. For T he takes the time of n oscillations with the stop watch of least count ∆T and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate?

If velocity of light c, acceleration due to gravity g and density d are the fundamental quantities in a system of measurement then mass has

E, m, L and G denote energy, mass, angular momentum and gravitational constant respectively, $\frac{{E{L^2}}}{{{m^5}{G^2}}}$ has the dimensions of

Taking frequency $f$, velocity $v$ and density $\rho$ to be the fundamental quantities, then the dimensional formula for momentum will be

The external and internal diameters of a hallow cylinder are measured to be $(4.23 \pm 0.01)\,cm$ and $(3.89 \pm 0.01)\,cm$. The thickness of the wall of the cylinder is