Units & measurements practice · Medium

When two quantities are divided, the relative error in the
result is given by

A physical quantity $Q$ is found to depend on observables $x, y$, and $z$, obeying relation $Q=x^3 y^2 / z$. The percentage error in the measurements of $x, y$, and $z$ are $1 \%, 2 \%$ and $4 \%$ respectively. What is percentage error in the quantity $Q$?

The dimensions of $(a \cdot b)$ in the equation $P=\frac{a-t^2}{b x}$ where $P$ is power, $x$ is distance and $t$ is time, are

The unit of absolute permittivity is

The heat generated in a circuit depends on resistance (R), current (I) and time of flow (t). If maximum errors in the above are 1%, 0.5%, 1% respectively error in measurement of power is ($P = {i^2}R$)

The unit of viscosity in the CGS system is poise (P) and that in $\mathrm{SI}$ is poiseuille (Pl). Which of the following statement is correct?

Light Year is a unit of

What is the SI unit of electron mobility?

Of the following quantities, which one has dimensions
different from the remaining three?

$\frac{{E}^2}{\mu_0}$ has the dimensions (${E}=$ electric field, $\mu_0=$ permeability of free space)

The number of significant figures in the numbers $4.8000 \times {10^4}$ and 48000.50 are respectively

Assertion : Force cannot be added to pressure.

Reason : Because their dimensions are different.

The unit of permittivity of free space ${\varepsilon _0}$ is

Statement I: The distance covered by a body is given by $s=u+\frac{1}{2} \frac{a}{t}$, where the symbols have usual meaning.

Statement II: We can add, substract or equate quantities which have same dimensions.

Which pair do not have equal dimensions?

The wrong unit conversion among the following is

Unit of electric flux is

A length is measured as $2500 \mathrm{~m}$ by a meter scale. Which of the following statement is correct:

What is the SI unit of surface tension?

If velocity (v), time (T) and mass (M) are taken as fundamental quantities, then dimensional formula for gravitational potential would be.

If muscle times speed equals power, what is the ratio of the SI units and the CGS unit of muscle?

If $\mu_0$ and $\varepsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \varepsilon_0}\right)$ is:

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

Which one of the following does not have the same dimensions

Error in the measurement of radius of a sphere is 1%. Then
error in the measurement of volume is

Which one of the following represents the correct dimensions of the coefficient of viscosity?

Dimensional equation cannot be used

The relation $\tan \theta=v^2 / r g$ gives the angle of banking of the cyclist going round the curve. Here $v$ is the speed of the cyclist, $r$ is the radius of the curve, and $g$ is the acceleration due to gravity. Which of the following statements about the relation is true?

A rectangular beam which is supported at its two ends and leaded in the middle with weight w sags by an amount δ such that $\delta = \frac{{w{l^3}}}{{4Y{d^3}}},\;$, where $l,d$ and Y represent length, depth and elasticity respectively. Guess the unknown factor using dimensional considerations

$\left[ {\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}} \right]$ are dimensions of