Units and Measurements

Which SI prefix represents the factor $10^{1}$?

What is the correct symbol for the SI unit 'mole'?

Which of the following is a derived SI unit?

Which base quantity is measured in Amperes ($A$)?

The unit of molar heat capacity in the SI system is:

Which SI prefix represents the multiplier $10^{12}$?

The value of the constant of proportionality in the SI system for Coulomb's law ($k = 1/4\pi\epsilon_0$) has the units:

A student derives a formula for the time period of a simple pendulum as $T = 2\pi \sqrt{\frac{g}{l}}$. Is this formula dimensionally correct?

The SI unit of permittivity of free space $\epsilon_0$ is:

The dimension of the ratio of magnetic flux ($\phi$) to electric flux ($\psi$) is:

The number of significant figures in $0.000010$ is:

Calculate $1.234 + 0.001$ and round to correct significant figures.

The number of significant figures in $0.001$ is:

Round off $4.845$ to three significant figures.

Calculate $1.23 / 0.5$ and round to the correct number of significant figures.

The number of significant figures in $100.01$ is:

Which of the following contains exactly three significant figures?

Express the number $0.0000000000000000001602$ in scientific notation with 4 significant figures.

Add $1.2 \times 10^3$ and $3.4 \times 10^2$.

The resistance $R = V/I$. If $V = 100.0 \pm 0.1 \text{ V}$ and $I = 10.00 \pm 0.01 \text{ A}$, then $R$ is:

In the equation $v = u + at$, the term 'at' must have the dimensions of:

The dimensions of solid angle are:

The dimensional formula for refractive index is:

What is the dimensional formula for the intensity of a wave (Energy per unit area per unit time)?

To verify the formula for the mechanical power $P$ delivered by a rotating torque $\tau$ at a constant angular velocity $\omega$, a student sets up the dimensional equation $P = k \tau^a \omega^b$. Using the dimensional formulas for each quantity as indicated in the flowchart, determine the value of the exponent $b$.

A student uses dimensional analysis to derive the relationship for the speed of sound $v$ in a gas, which depends on the pressure $P$ of the gas and its density $\rho$ as $v = k P^x \rho^y$. Following the logic of the principle of dimensional homogeneity shown in the flowchart, what are the correct values for the exponents $x$ and $y$?

The dimensional formula of the universal gravitational constant $G$ is:

Find the dimensions of $\frac{a}{b}$ in the equation $P = \frac{a - x^2}{bt}$ where $P$ is pressure, $x$ is distance, and $t$ is time.

If the energy of a photon is given by $E = h f$, where $f$ is frequency, the dimensions of Planck's constant $h$ are:

The dimensional formula of 'modulus of rigidity' is same as that of:

Which of these is the correct formula for Mean Absolute Error ($\Delta a_{mean}$)?

Errors that occur due to the carelessness of the observer are:

If $y = x^n$, then $\Delta y / y$ is equal to:

The sum of several measurements divided by the number of measurements gives the:

The mass of a body is $(2.000 \pm 0.001) \text{ g}$. The percentage error in the mass is:

Which of the following is the most accurate value of a length of $5 \text{ cm}$ measured by different instruments?

The zero error of a vernier calliper is said to be negative if:

In a calculation $Z = A/B$, if the percentage error in $A$ is $x\%$ and the percentage error in $B$ is $y\%$, then the percentage error in $Z$ is:

If the value of resistance is $10.845 \Omega$ and the value of current is $3.23 \text{ A}$, the value of potential difference up to appropriate significant figures is:

The percentage error in the measurement of mass and speed are $2\%$ and $3\%$ respectively. The maximum error in the estimation of momentum is:

Which of the following is the dimension for spring constant?

The dimensions of velocity gradient are:

Dimensional formula of thermal conductivity is:

The dimensional formula for moment of inertia is:

The dimensions of 'Moment of Inertia' are:

The dimensions of 'Intensity of Wave' (energy per unit area per unit time) are:

What is the dimensional formula for 'Torque per unit twist'?

A physical quantity $Q$ is derived through a series of operations involving the coefficient of viscosity $\eta$, the mass density $\rho$, and the surface tension $S$, as illustrated in the flowchart. Based on the sequence of operations, what is the dimensional formula for the quantity $Q$?

The dimensions of 'Hubble's Constant' are:

The dimensional formula for 'Electric Dipole Moment' is:

The dimensions of Energy are:

Dimensional formula for Volume is:

In the equation $F = at + bt^2$, where $F$ is force and $t$ is time, what is the dimension of $a$?

The dimensional formula of Velocity Gradient is:

The dimensions of the ratio of linear momentum to angular momentum are:

The dimensional formula of 'entropy' is:

Which of the following physical quantities has the dimensions $[M L^2 T^{-3}]$?

In a theoretical physics model, a researcher decides to use Power ($P$), Acceleration ($a$), and Frequency ($f$) as the fundamental base units. Based on the relationship shown in the flowchart, which of the following combinations represents the correct dimensional formula for Mass ($M$) in this system?

What are the dimensions of $X$ in the equation $Force = X / \text{Density}$?

Dimensions of Torque are same as that of: