Units & measurements practice · Medium

If $S = \frac{1}{3}f{t^3},f$ has the dimensions of

We can reduce random errors by

If error in radius is 3%, what is error in volume of sphere?

The dimensional formula for impulse is

Which of the following is the smallest unit

Instrumental error can be caused due to

The physical quantity having the dimensions $\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 3}}{\mathrm{A}^2}{T^3}} \right]$ is

A spectrometer gives the following reading when used to measure the angle of a prism Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

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

The power of lens is $P = \frac{1}{f},\;$ where f is focal length of the lens . The dimensions of power of lens are

The dimensional formula of relative density is

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are

Faraday is the unit of

A physical quantity P is given by $P = \frac{{{A^3}{B^{\frac{1}{{\;2}}}}}}{{{C^{ - 4}}{D^{\frac{3}{2}}}}}.$. The quantity which brings in the maximum percentage error in P is

The equation of a wave is given by $Y\; = \;A\sin \omega \left( {\begin{array}{cccccccccccccccccccc} {\frac{x}{\upsilon } - k}\\ \; \end{array}} \right)$ where $\omega$ is the angular velocity and υ is the linear velocity. The dimension of k is

When a wave traverses a medium, the displacement of a particle located at x at a time t is given by $y = a\sin \left( {bt - cx} \right)$, where a,b and c are constants of the wave. Which of the following is a quantity with dimensions

Unit of electric flux is

Which of the following equations is dimensionally incorrect?
Where, $t$ = time, $h$ = height , $s$ = surface tension, $\theta$ = angle, $\rho =$ density, $a,r$ = radius, $g$ = acceleration due to gravity, $V$ = Volume, $P$ = presssure, $W$ = Work done, $\tau =$ torque, $\varepsilon =$ permittivity, $E$ = Electric field, $J$ = Current density, $L$ = length

Which of the following is dimensionally correct

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\sin ct + b\cos \,dx$, then the dimension of $a/b$ is:-

IF R and L represents resistance and inductance respectively, which of the following combination has the dimensions of frequency

We can compensate backlash error by:

In the formula, $a = 3b{c^2},a$ and c have dimensions of electric capacitance and magnetic induction respectively. What are dimensions of b in MKS system?

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage
supply are

The dimensional formula for $\omega$ in the relation $y = A\sin \omega t$ is

$1\mathrm{\;Wb}/{\mathrm{m}^2}$ is equal to

Which of the following five physical parameters have the same dimensions (A) Energy density (B) Refractive index (C) Dielectric constant (D) Young’s modulus (E) Magnetic field

Assertion: Out of three measurements $l=0.7 \mathrm{~m}$; $l=0.70 \mathrm{~m}$ and $l=0.700 \mathrm{~m}$, the last one is most accurate.

Reason: In every measurement, only the last significant digit is not accurately known.

If $R, X_{L}$ and $X_{c}$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless

The order of magnitude of diameter of earth $\left(1.28 \times 10^7 \mathrm{~m}\right)$ is