JEE Main 2022 Question Paper (27-Jul-2022) (Shift 2)

Question 1

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

Accepted Answer

$\left[\mathrm{M}^0 \mathrm{L}^2 \mathrm{T}^0\right]$

Answer

$\left[\mathrm{ML}^2 \mathrm{T}^{-2} 	heta^{-1}ight]$

Answer

$\left[\mathrm{M}^0 \mathrm{L}^2 \mathrm{T}^{-2}\right]$

Answer

$\left[ \mathrm{M}^0 \mathrm{L}^0 \mathrm{T}^0 \right]$

Question 2

A body of mass $10 \ \mathrm{kg}$ is projected at an angle of $45^\circ$ with the horizontal. The trajectory of the body is observed to pass through a point $\left(20,10\right)$. If $T$ is the time of flight, then its momentum vector, at time $t = \frac{T}{\sqrt{2}}$, is _____ .
[Take $g = 10 \ \mathrm{m} \ \mathrm{s}^{-2}$]

Accepted Answer

$100\sqrt{2}\hat{\mathrm{i}} + \left(100\sqrt{2} - 200\right)\hat{\mathrm{j}} \quad \mathrm{N} \cdot \mathrm{s}$

Answer

$100\hat{\mathrm{i}} + \left(100\sqrt{2} - 200\right)\hat{\mathrm{j}} \quad \mathrm{N} \cdot \mathrm{s}$

Answer

$100\sqrt{2}\hat{\mathrm{i}} + \left(100 - 200\sqrt{2}\right)\hat{\mathrm{j}} \quad \mathrm{N} \cdot \mathrm{s}$

Answer

$100\hat{\mathrm{i}} + \left(100 - 200\sqrt{2}\right)\hat{\mathrm{j}} \quad \mathrm{N} \cdot \mathrm{s}$

Question 3

A block of mass $M$ slides down on a rough inclined plane with constant velocity. The angle made by the inclined plane with the horizontal is $	heta$. The magnitude of the contact force will be:

Accepted Answer

$Mg$

Answer

$ Mg \cos 	heta $

Answer

$ \sqrt{Mg \sin 	heta + Mg \cos 	heta} $

Answer

$ Mg \sin 	heta \sqrt{1 + \mu} $

Question 4

A block $ A $ takes $ 2 \ \mathrm{s} $ to slide down a frictionless incline of $ 30^\circ $ and length $ l $, kept inside a lift going up with uniform velocity $ v $. If the incline is changed to $ 45^\circ $, the time taken by the block to slide down the incline will be approximately:

Accepted Answer

$1.68 \quad \mathrm{s}$

Answer

$2.66 \quad \mathrm{s}$

Answer

$0.83 \quad \mathrm{s}$

Answer

$0.70 \quad \mathrm{s}$

Question 5

The velocity of the bullet becomes one third after it penetrates $4 \quad \mathrm{cm}$ in a wooden block. Assuming that the bullet is facing a constant resistance during its motion in the block, the bullet stops completely after travelling a distance of $(4 + x) \, \mathrm{cm}$ inside the block. The value of $x$ is

Accepted Answer

$0.5$

Answer

$2.0$

Answer

$1.0$

Answer

$1.5$