Units & measurements practice · Easy

Which of the following statement(s) is/are correct?
I. A screw gauge having a smaller value of pitch has greater accuracy.
II. The least count of screw gauge is directly proportional to the number of divisions on circular scale.

Zero error is a/an

Statement-I: In the measurement of $g$ using simple pendulum generally we take central position (mean position) of the oscillation as reference position for measuring time of oscillation.
Statement-II: This reduces the human error in measurement of time.

Statement-I: Electric current is a scalar
Statement-II: All fundamental physical quantities are scalars

The equation of stationary wave is: $y=2 a \sin \left(\frac{2 \pi n t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right)$. Which of the following is NOT correct

Which of the following sets of quantities have same dimensional formula?

Dimensions of kinetic energy are

The unit of expression ${\mathrm{\mu }_0}{\mathrm{\varepsilon }_0}$ are

Which of the following is not the unit of energy

Statement-I: If a physical quantity has a unit, it must not be dimensionless.
Statement-II: No physical quantity exists which has dimension but no unit.

Which of the following quantities has the same dimensions as that of energy

Unit of stress is

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.

Assertion The error in the measurement of radius of the sphere is $0.3 \%$. The permissible error in its surface area is $0.6 \%$.

Reason The permissible error is calculated by the formula $\frac{\Delta A}{A}=4 \frac{\Delta r}{r}$

The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of it’s volume is

If $p=\frac{R T}{V-b} e^{-\alpha V / R T}$, then dimensional formula of $\alpha$ is

A physical quantity $Q$ is calculated according to the expression

$Q=\frac{A^3 B^3}{C \sqrt{D}}$

If percentage errors in $A, B, C, D$ are $2 \%, 1 \%, 3 \%$ and $4 \%$, respectively. What is the percentage error in $Q$ ?

Using mass $(M)$, length $(L)$, time $(T)$ and current $(A)$ as fundamental quantities, the dimensions of permeability are

Which pair has the same dimensions

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

If e is the charge, $\mathrm{V}$ the potential difference, $\mathrm{T}$ the temperature, then the units of $\frac{\mathrm{eV}}{\mathrm{T}}$ are the same as that of

Which of the following the same dimensions ?

Choose the incorrect options among the following

A physical quantity $\mathrm{T}=\frac{\sqrt{\mathrm{abc}^2}}{\mathrm{~d}^3 \mathrm{e}^{1 / 6}}$ is determined by measuring a, b, c, d, e separately with the percentage error of $1 \%, 2 \%, 3 \%, 4 \%, 3 \%$ respectively. Minimum amount of error is contributed by the measurement of :

The unit of specific resistance is

The value of Planck's constant is

Statement-I: Plane angle is a dimensionless quantity.
Statement-II: All supplementary quantíties are dimensionless.

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

The dimensional formula of farad is

Statement-I : If $u_1$ and $u_2$ are units and $n_1, n_2$ are their numerical values in two different systems then $n_1 > n_2 \Rightarrow u_1 < u_2$.
Statement-II: The numerical value of physical quantity is inversely proportional to unit.