Units & measurements practice · Mixed difficulty

Statement I: The order of accuracy of measurement depends on the least count of the measuring instrument.

Statement II: The smaller the least count, the greater is the number of significant figures in the measured value.

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

Given a charge $q,$ current $I$ and permeability of vacuum $\mu_0.$ Which of the following quantity has the dimension of momentum?

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

The force F on the sphere of radius ‘a’ moving in a medium with velocity '$v$' is given by $F = 6\pi \eta a\upsilon$. The dimensions of η are

If a current of 2.33 amp is passes through a resistance of 10.485 ohm, the potential is 24.43005 V its value is proper significant figures would be

If the unit of force is $\mathrm{kN}$, the length is $1 \mathrm{~km}$ and time $100 \mathrm{~s}$, then what will be the unit of mass?

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

What is dimensional formula of thermal conductivity?

$erg - {m^{ - 1}}$ can be the unit of measure for

Which of the following is not equal to watt

Assertion: The percentage change in time period is $1.5 \%$, if the length of simple pendulum increases by $3 \%$.
Reason: Time period is directly proportional to length of pendulum.

The area of a rectangular field (in ${m^2}$) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is :

The dimensions of K in the equation $W = \frac{1}{2}\;K{x^2}$ is

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

In the determination of Young’s modulus $\left( {Y = \frac{{4\;MLg}}{{\pi \;\ell {d^2}}}} \right)$ by using Searle’s method, a wire of length L=2m and diameter d=0.5mm is used. For a load M=2.5 kg, an extension $\ell = 0.25mm$ in the length of the wire is observed. Quantities d and $\ell$ are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable scale is 100. The contributions to the maximum probable error of the Y measurement

Given that $r = {m^2}$ sin pt, where t represents time. If the unit of m is N, then the unit of r is

Parsec is a unit of

Choose the incorrect options among the following

Which of the following physical quantities has neither dimensions nor unit?

Which is different from others by units

The dimensions of $(\text { velocity })^2 \div$ radius are the same as that of

The dimensional formula of angular velocity is

The dimensions of ${e^2}/4\mathrm{\pi }{\mathrm{\varepsilon }_0}hc,$, where $e,\;{\mathrm{\varepsilon }_0},\mathrm{\;}h\;\mathrm{and\;}c$ are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively, are

The radius of the sphere is $\left( {4.3 \pm 0.1} \right)$ cm. The percentage error in its volume is

Which of the following system of units is not based on units of mass, length and time alone

There are atomic clocks capable of measuring time with an accuracy of 1 part in ${10^{11}}$. If two such clocks are operated with precision, then after running for 5000 years, these will record

If the velocity of light $\left( C \right)$ gravitational constant $\left( G \right)$ and Planck’s constant $h$ are chosen as fundamental units,then the dimensions of mass in new system is