Units & measurements practice · Mixed difficulty

Which of the following quantities can have SI unit $\mathrm{kg} \mathrm{~m}^2 \mathrm{~A}^{-2} \mathrm{~s}^{-3}$.

The wavelength associated with a moving particle depends upon power p of its mass m, qth power of its velocity v and rth power of planck’s constant h. Then the correct set of values of p,q and r is

The value of 0.99-0.989 is

For a real gas the equation of gas is given by $\left(P+\frac{a n^2}{V^2}\right)(V-b n)=n R T$. If symbols have their usual meaning, then the dimensions of $\frac{v^2}{a n^2}$ is same as that of

Unit of moment of inertia in MKS system

What will be dimensions of $a$ in the formula $p=\left(p_0+a\right)(b+t)$ here $p=$ pressure, $t=$ time, and $x=$ distance:

$M{L^3}{T^{ - 1}}{Q^{ - 2}}$ is dimensions of

Which of the following physical quantities have the
same dimensions?

A physical quantity $x$ depends on quantities $y$ and $z$ as $\,x = Ay + B\,\,\,\sin \,\,\,\,(Cz),\,$ where $A,\,\,B$ and $C$ are constants. Which of the following have same dimensions?

Calculate $z$ for the following case.
$z=(x-2.5 y+w)$ for $x=(4.72 \pm0.12) \mathrm{m}, {y}=(4.4 \pm 0.2) \mathrm{m}, {w}=(15.63\pm 0.16) \mathrm{m}$.

With the usual notations, the following equation ${S_t} = u + \frac{1}{2}a\left( {2t - 1} \right)\;$ is

In a metre bridge experiment, we try to obtain the null point at the middle. This:

The dimensions of gravitational constant G and the moment of inertia are respectively

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is:

The dimensions of calorie are

Assertion: A dimensionless quantity may have unit.

Reason: Two physical quantities having same dimensions, may have different units.

Dimensional formula for force is

The unit of magnetic moment is

Size of universe is about

Which one of the following represents the correct dimensions of the quantity: $x=\frac{\eta}{\rho}$, where
$\eta=$ coefficient of viscosity and $\rho=$ the density of a liquid?

The unit of self inductance of a coil is

The number of significant figures in 0.02300 is

The voltage and current in a conductor are measured as $(50 \pm 2) V$ and $(5 \pm 0.2) A$. The percentage error in the calculation of resistance is

The dimensions of emf in MKS is

Let us choose a new unit of length such that the velocity of light in vacuum is unity. If light takes 8 min and 20 sec to cover the distance between sun and earth, this distance in terms of the new unit is

Volume of liquid flowing per second through a capillary tube is given by $\mathrm{V}=\frac{\mathrm{K}\left[\mathrm{x}_2-\mathrm{x}_1\right]^4}{\left[\mathrm{y}_2-\mathrm{y}_1\right]}$ where $x_1$ and $x_2$ are inner and outer radii and $y_2$ and $y_1$ are positions crossed by the liquid. The dimensional formula for $\mathrm{K}$ is :-

How many wavelengths of $K{r^{86}}\mathrm{\;}$ are there in one metre

The number of significant figures in all the given number 25.12, 2022, 4.389, and $1.812 \times {10^{ - 6}}$ is

If the digit to be dropped is more than 5, then the preceding digit is _____.

One shake is equal to