Units & measurements practice · Medium

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

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 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

Statement I: The dimensional method cannot be used to obtain the dependence of the work done by a force $F$ on the angle $\theta$ between force $F$ and displacement $x$.

Statement II: Angle can be measured in radians but it has no dimensions.

The dimension of torque is

Which of the following pairs has the dimensions of length?

Dimensions of coefficient of viscosity are

The dimensions $\left[\mathrm{ML}^2 \mathrm{T}^{-2} \mathrm{A}^{-1}\right]$ belong to the:

The ratio of S.I unit of universal gravitational constant to C.G.S unit is

Farad is not equivalent to

The potential energy of a particle that varies with distance ${x}$ is ${V}(x)=-\alpha x+\beta \sin \frac{x}{\gamma}$. A dimensionless combination of constants $\alpha, \beta, \gamma$ is

Dimensional formula of heat energy is