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A student in the laboratory measures thickness of a wire using screw gauge. The readings are $ 1.22 \, \text{mm} $, $ 1.23 \, \text{mm} $, $ 1.19 \, \text{mm} $ and $ 1.20 \, \text{mm} $. The percentage error is $ \frac{x}{121} \% $. The value of $ x $ is ________.

The dimensions of $ \left( \dfrac{B^{2}}{\mu_{0}} \right) $ will be:
(if $ \mu_{0} $ : permeability of free space and $ B $ : magnetic field)

Identify the pair of physical quantities that have same dimensions:

Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A): Time period of oscillation of a liquid drop depends on surface tension $ (S) $, if density of the liquid is $ \rho $ and radius of the drop is $ r $, then $ T = K \sqrt{\dfrac{\rho r^{3}}{S^\dfrac{3}{2}}} $ is dimensionally correct, where $ K $ is dimensionless.
Reason (R): Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

An expression of energy density is given by $ u = \dfrac{\alpha}{\beta}\sin\!\left(\dfrac{\alpha x}{k t}\right) $, where $ \alpha, \beta $ are constants, $ x $ is displacement, $ k $ is Boltzmann constant and $ t $ is the temperature. The dimensions of $ \beta $ will be:

Given below are two statements: One is labelled a Assertion A and the other is labelled as Reason R.

Assertion A: Product of Pressure ($P$) and time ($t$) has the same dimension at that of coefficient of viscosity.
Reason R: $\text{Coefficient of viscosity} = \frac{\text{Force}}{\text{Velocity gradient}}$.

Choose the correct answer from the options given below:

The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be:

Which of the following physical quantities have the same dimensions?

The dimension of mutual inductance is:

10.

If momentum $ [P] $, area $ [A] $ and time $ [T] $ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

11.

For $ z = a^{2} x^{3} y^{\frac{1}{2}} $, where '$ a $' is a constant. If percentage error in measurement of '$ x $' and '$ y $' are $ 4\% $ and $ 12\% $, respectively, then the percentage error for '$ z $' will be ____________ $ \% $.

12.

Identify the pair of physical quantities which have different dimensions:

13.

Match List I with List II.

List I	List II
A. Torque	I. $ \mathrm{N\,m\,s^{-1}} $
B. Stress	II. $ \mathrm{J\,kg^{-1}} $
C. Latent Heat	III. $ \mathrm{N\,m} $
D. Power	IV. $ \mathrm{N\,m^{-2}} $

Choose the correct answer from the options given below:

14.

The distance of the Sun from earth is $ 1.5 \times 10^{11} \, \text{m} $ and its angular diameter is $ (2000) \, s $ when observed from the earth. The diameter of the Sun will be:

15.

If $ L $, $ C $ and $ R $ are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

16.

An expression for a dimensionless quantity $ P $ is given by $ P = \frac{\alpha}{\beta} \log_e \left( \frac{k t}{\beta x} \right) $; where $ \alpha $ and $ \beta $ are constants, $ x $ is distance; $ k $ is Boltzmann constant and $ t $ is the temperature. Then the dimensions of $ \alpha $ will be:

17.

Velocity $ (v) $ and acceleration $ (a) $ in two systems of units $ 1 $ and $ 2 $ are related as $ v_2 = \frac{n}{m^2} v_1 $ and $ a_2 = \frac{a_1}{mn} $ respectively. Here $ m $ and $ n $ are constants. The relations for distance and time in two systems respectively are:

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JEE Main 2022 25th July Morning Shift

Which of the following physical quantities have the same dimensions?

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JEE Mains JEE Advance BITSAT
JEE Mains | PYQ