List of top Physics Questions on Dimensional Analysis asked in KEAM

Which one of the following physical quantities has dimensions?
In the equation $A = \dfrac{B}{CD^2}$, if $B, C$ and $D$ have the dimensions of inductive reactance, capacitive reactance and angular frequency respectively, then the dimensions of $A$ are:
The physical quantity that doesn’t have appropriate unit is
Time period of a particle is \( T = k\sqrt{\frac{\rho r^3}{\sigma}} \), where \( k \) is a dimensionless constant, \( \rho \) is density, and \( r \) is radius. The dimension of \( \sigma \) is same as
The dimensions for the gravitational constant $G$ are ____.
The dimension of $X$ in the equation $F=6\pi\eta X$ is: (F - Force; $\eta$ - Coefficient of viscosity)
\( [L^0 M^0 T^{-1}] \) is the dimensional formula for
The dimensional formula for the product of moment of inertia and the square of angular velocity is
If \(\varepsilon_0\) and \(\mu_0\) are respectively the electrical permittivity and magnetic permeability of vacuum, the dimensional formula for \(\dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}\) is
The power in an electrical circuit for a current of \(5 \pm 0.4\text{ A}\) and voltage \(10 \pm 0.2\text{ V}\) is measured at \(10%\) error. To measure the power at \(5%\) error the current should be measured at an error of
The angular diameter of a planet measured from earth is \(90''\). If the diameter of the planet is \(x \times 10^4\) m, then its distance from the earth is
The standard of length is maintained by a 1 meter long bar made up of a material having coefficient of linear expansion \( \alpha = 10^{-5}\,\text{°C}^{-1} \). If the length of the bar were to be preserved to an accuracy of 1 part per million, what would be the maximum allowed temperature variation?
The dimension of mutual inductance is (Denote dimension of current as A)
The dimensions for pressure is:
A person observes that the full length of a train subtends an angle of $15^\circ$. If the distance between the train and the person is $3$ km, the length of the train, calculated using parallax method, in meters is
When the voltage and current in a conductor are measured as $(100 \pm 4)$ V and $(5 \pm 0.2)$ A, then the percentage of error in the calculation of resistance is
A force F is applied onto a square plate of side L. If the percentage error in determining L is 2% and that in F is 4%, the permissible percentage error in determining the pressure is
In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time-period is 3%. Then the maximum percentage error in determination of the acceleration due to gravity \( g \) is
The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively
The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively
In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time-period is 3%. Then the maximum percentage error in determination of the acceleration due to gravity \( g \) is
In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time-period is 3%. Then the maximum percentage error in determination of the acceleration due to gravity \( g \) is
The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively