Units & measurements practice · Mixed difficulty

Taking into account the significant figures, what should be the value of 9.99 + 0.0099?

Assertion: All derived quantities may be represented dimensionally in terms of the base quantities.
Reason : The dimensions of a base quantity in other base quantities are always zero.

If h is plank’s constant and $\lambda$ is the wave length, $\frac{h}{\lambda }$ has the dimensions of

Assertion: In the measurement of physical quantities direct and indirect methods are used.

Reason : The accuracy and precision of measuring instruments along with errors in measurements should be taken into account, while expressing the result.

Illuminance of a surface is measured in

In the following list, the only pair which have different dimensions, is

Dimensions of planck’s constant is:

Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are

Which of the following units denotes the dimensions $\left[ {\mathrm{M}{\mathrm{L}^2}/{\mathrm{Q}^2}} \right],$, where Q denotes the electric charge?

If the percentage error in measuring length and diameter of a wire is $0.1 \%$ each, then the percentage error of the resistance of the wire is

Which of the following quantity is NOT dimensionless?

The radius of a uniform wire is $r=0.021 \mathrm{~cm}$. The value of $\pi$ is given to be 3.142. What is the area of cross-section of the wire up to appropriate significant figures?

Which of the following is dimensionally correct

If the value of the resistance is 10.845Ω and the value of the current is 3.23 A, then the potential difference is 35.02935 V. its value in correct significant figures would be

Given below are two statements.

Statement (I): Dimensional formula of planck's constant is $\left[M L^2 T^{-1}\right]$

Statement (II): Dimensional formula of bulk modulus is $\left[M L^{-1} T^{-2}\right]$

The dimensions of surface tension are

Estimate the mean absolute error from the following data: $20.17,21.23,20.79,22.07,21.78$:

Which of the following pair have same dimensional formula?

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.

Which of the following do not have the same dimensional formula as the velocity?
Given that $\mathrm{m}_0=$ permeability of free space, $\mathrm{e}_0=$ permittivity of free space, $\mathrm{n}$ = frequency, $l$ = wavelength, $\mathrm{P}=$ pressure, $\mathrm{r}$ $=$ density, $\mathrm{w}=$ angular frequency, $\mathrm{k}=$ wave number

Zero error is a/an

In the equation $\left[X+\frac{a}{Y^{2}}\right][Y-b]=R T, \, X$ is pressure, $Y$ is volume, $R$ is universal gas constant $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:

Velocity of sound in a medium is given by ${A^{1/2}}\,{d^{ - 1/2}}$ where $d$ is density of medium. Then $A$ represents

In the relation $x = \cos \left( {\omega t + kx} \right)$, the dimension(s) of $\omega$ is/are

Dimensions of specific heat are

Write the dimensions of $a b$ in the relation $\mathrm{P}=\frac{\mathrm{a}-\mathrm{t}^2}{\mathrm{bx}}$, where $\mathrm{P}$ is the pressure, $\mathrm{x}$ is the distance and $t$ is the time.

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.

If C is the restoring couple per unit radian twist and I is the moment of inertia, then the dimensional representation of $2\mathrm{\pi }\sqrt {\frac{I}{C}}$ will be

Assertion : Parallex method cannot be used for measuring distances of stars more than 100 light years away.

Reason : Because parallex angle reduces so much that it cannot be measured accurately.

Assertion: Formula for kinetic energy is $\mathrm{K}=\frac{1}{2} \mathrm{mu}^2=\mathrm{ma}$

Reason : Both the equation $\mathrm{K}=\frac{1}{2} \mathrm{mv}^2$ and $\mathrm{k}=\mathrm{ma}$ are dimensionally incorrect.