JEE Main 2022 Question Paper (28-Jul-2022) (Shift 2)

Question 1

Consider the efficiency of Carnot's engine given by $ \eta = \frac{\alpha \beta}{\sin 	heta} \log_{e} \frac{\beta x}{k T}, $ where $\alpha$ and $\beta$ are constants. If $T$ is temperature, $k$ is Boltzmann constant, $	heta$ is angular displacement, and $x$ has the dimensions of length, then choose the incorrect option.

Accepted Answer

Dimensions of $ \alpha $ is same as that of $ \beta $

Answer

Dimensions of $ \beta $ is same as that of force.

Answer

Dimensions of ${\alpha}^{-1} x$ is the same as that of energy.

Answer

Dimensions of $ \eta^{-1} \sin 	heta $ is same as that of $ \alpha \beta $

Question 2

At time $ t=0 $ a particle starts travelling from a height $ 7\hat{\mathrm{z}} $ cm in a plane keeping the $ z $ coordinate constant. At any instant of time, its position along the $ x $ and $ y $ directions are defined as $ 3t $ and $ 5t^{3} $ respectively. At $ t=1 $ s, the acceleration of the particle will be

Accepted Answer

$30y$

Answer

$-30y$

Answer

$3x + 15y$

Answer

$3x + 15y + 7\hat{z}$

Question 3

A pressure-pump has a horizontal tube of cross-sectional area $10  \mathrm{cm}^2$ for the outflow of water at a speed of $20  \mathrm{m}  \mathrm{s}^{-1}$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube is: [given: density of water $= 1000  \mathrm{kg} \quad \mathrm{m}^{-3}$]

Accepted Answer

$400 \quad \mathrm{N}$

Answer

$300 \quad \mathrm{N}$

Answer

$500 \quad \mathrm{N}$

Answer

$250 \quad \mathrm{N}$

Question 4

A uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ hanging on one side and the rest of its length $L - l$ hanging on the other side of the pulley. At a certain point of time, when $l = \frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is _____.

Accepted Answer

$4$

Answer

$6$

Answer

$2$

Answer

$1.5$

Question 5

A bullet of mass $200  \mathrm{g}$ having initial kinetic energy $90  \mathrm{J}$ is shot inside a long swimming pool as shown in the figure. If its kinetic energy reduces to $40  \mathrm{J}$ within $1  \mathrm{s}$, the minimum length of the pool the bullet has to travel so that it completely comes to rest is

Accepted Answer

$45\,\mathrm{m}$

Answer

$90\,\mathrm{m}$

Answer

$125\,\mathrm{m}$

Answer

$25\,\mathrm{m}$