Units & measurements practice · Mixed difficulty

Which pair has the same dimensions

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

If the length of a cylinder is measured to be 50 cm with an error of 0.25 cm. The percentage error in the measured length is

A quantity $x$ is defined as $x=\frac{a^3-b^2}{\sqrt{c+d}}$. Value of $a, b, c$ and $d$ are reported as ${a}=3 \pm 0.001, {b}=5 \pm 0.0013, {c}=6 \pm 0.24$ and ${d}=10 \pm 0.4$. Percentage error in ${x}$ will be-

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

The value of two resistors are ${R_1} = (6 \pm 0.3)k\,\Omega$ and ${R_2} = (10 \pm 0.2)k\,\Omega.$ The percentage error in the equivalent resistance when they are connected in parallel is

The dimensions of shear modulus are

The angle of $1^{\prime}$ (minute of arc) in radian is nearly equal to

The unit of self inductance of a coil is

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

The speed (v) of ripples on the surface of water depends on surface tension ($\sigma$), density ($\rho$) and wavelength ($\lambda$). The square of speed (v) is proportional to

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

The number of significant figures in a number
"1700.00200" is

The dimensional formula of relative density is

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 unit of Wien’s constant b is

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

Which relation is wrong

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

The de-Broglie wavelength associated with a particle of mass $\mathrm{m}$ and energy $\mathrm{E}$ is $\mathrm{h} / \sqrt{\mathrm{2 m E}}$. The dimensional formula for Planck's constant is :

Data for four screwgauge's given below, arrange them increasing order of accuracy.
(a) Pitch $=1 \mathrm{~mm}$, no. of division on C.S. $=100$
(b) Pitch $=0.5 \mathrm{~mm}$, no. of division on C.S. $=100$
(c) Pitch $=3 / 4 \mathrm{~mm}$, no. of division on C.S. $=60$
(d) Pitch $=1 / 2 \mathrm{~mm}$, no. of division on C.S. $=50$