List of top Physics Questions on Units, Dimensions and Measurements

Find the dimensions of √(G h c⁵).

If \(R=\) resistance, \(L=\) inductance, \(C=\) capacitance, then the dimension \([ML^2T^{-4}A^{-2}]\) represents

In a vernier caliper, 1 main scale division equals \(1\,\text{mm}\) and \(9\) MSD are divided into \(10\) equal parts by the vernier scale. When nothing was present in the jaws, zero of the vernier scale lies to the right of zero of the main scale and the \(7^{th}\) division of vernier scale coincides with one of the main scale divisions. Find zero error in the vernier caliper.

Consider a modified Bernoulli equation. \[ P + \frac{A}{Bt^2} + \rho g(h + Bt) + \frac{1}{2} \rho v^2 = \text{constant} \] If t has the dimension of time then the dimensions of A and B are_________ respectively.

In an experiment the values of two spring constants were measured as \(k_1 = (10 \pm 0.2)\) N/m and \(k_2 = (20 \pm 0.3)\) N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is:

A quantity \( X \) is given by \[ X=\varepsilon_0 L \frac{\Delta V}{\Delta t}, \] where \( \varepsilon_0 \) is permittivity of free space, \( L \) is length, \( \Delta V \) is potential difference and \( \Delta t \) is time interval. The dimension of \( X \) is same as that of

A ball of radius r and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time t, given by $t = A \rho^a r^b \eta^c \sigma^d$, where A is a constant and a, b, c and d are integers. The value of $\frac{b+c{a+d}$ is ___.}

Time taken to achieve terminal velocity by a body depends on density of material (\(\rho\)), density of liquid (\(\sigma\)), radius of material (r) and viscosity of liquid (\(\eta\)) as \(t = k\rho^a r^b \eta^c \sigma^d\). Find \(\frac{b+c}{a+d}\) ?

What will be the number of significant figures in the summation of \(0.153,\; 153.2\) and \(153.2\)?

If nothing is kept between jaws, zero of Vernier scale lies right of 0 cm of main scale and \(4^{th}\) line of Vernier scale matches perfectly with any line of main scale. An object is kept between jaws and zero of Vernier scale crosses \(15^{th}\) division of main scale and \(5^{th}\) division of Vernier scale exactly matches with any line of main scale. (Least count = 0.1 mm and 1 MSD = 1mm). Find dimension of object :

Column-I gives physical quantities and Column-II represent their dimensions. Choose the option representing correct matching.

Two springs have spring constants
$k_{1} = (40 \pm 0.4)$ N/m and
$k_{2} = (60 \pm 0.6)$ N/m.
If they are connected in parallel, the percentage error in the equivalent spring constant is:

Match the columns:

Choose the correct option.

A physical quantity is represented by $P = X^aY^bZ^c$. If the errors in the measurements of the physical quantities X, Y and Z are respectively a%, b% and c%, then the percentage error in the determination of quantity P is

Which of the following quantity has the same dimensions as \( \sqrt{\frac{\mu_0}{\epsilon_0}} \)?

A fractional errors in $x$, $y$, and $z$ are $0.1$, $0.2$, and $0.5$ respectively. Find the maximum fractional error in $x^{-2} y^3 z^{-2}$.

Match List-I with List-II.

Choose the correct answer from the options given below:

The Power \( P \) radiated from an accelerated charged particle is given by \( P \propto \left( \frac{q a}{c^n} \right)^m \), where \( q \) is the charge, \( a \) is the acceleration, and \( c \) is the speed of light in vacuum. From dimensional analysis, the value of \( m \) and \( n \) respectively are:

Given below are two statements:
Statements 1: Astronomical unit (AU), Parsec (pc) and Light year (ly) are units for measuring astronomical distances.
Statement 2: The light of the above distances, choose the most appropriate answer from the options given below: