JEE Main 2022 Question Paper (29-Jun-2022) (Shift 1)

Question 1

Two balls $ A $ and $ B $ are placed at the top of a $ 180  \mathrm{m} $ tall tower. Ball $ A $ is released from the top at $ t = 0  \mathrm{s} $. Ball $ B $ is thrown vertically down with an initial velocity $ u $ at $ t = 2  \mathrm{s} $. After a certain time, both balls meet $ 100  \mathrm{m} $ above the ground. Find the value of $ u $ in $ \mathrm{m}  \mathrm{s}^{-1} $. [use $ g = 10  \mathrm{m}  \mathrm{s}^{-2} $]

Accepted Answer

$30$

Answer

$10$

Answer

$15$

Answer

$20$

Question 2

A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1:1:2$. Two smaller pieces fly off perpendicular to each other with velocities of $30\, \mathrm{m\, s}^{-1}$ and $40\, \mathrm{m\, s}^{-1}$ respectively. The velocity of the third piece will be

Accepted Answer

$25\quad \mathrm{m} \quad \mathrm{s}^{-1}$

Answer

$35\quad \mathrm{m} \quad \mathrm{s}^{-1}$

Answer

$50\quad \mathrm{m} \quad \mathrm{s}^{-1}$

Answer

$15 \quad \mathrm{m} \quad \mathrm{s}^{-1}$

Question 3

The activity of a radioactive material is $2.56 \times 10^{-3} \, \mathrm{Ci}$. If the half-life of the material is 5 days, after how many days will the activity become $2 \times 10^{-5} \, \mathrm{Ci}$?

Accepted Answer

$35$ days

Answer

$30$ days

Answer

$40$ days

Answer

$25$ days

Question 4

A spherical shell of mass $1 \quad \mathrm{kg}$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane (as shown in the figure). The magnitude of the angular momentum of the shell about the origin $O$ is $\frac{a}{3} R^{2} \omega$. The value of $a$ will be

Accepted Answer

$5$

Answer

$2$

Answer

$3$

Answer

$4$

Question 5

A cylinder of fixed capacity of $44.8$ litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of the gas in the cylinder by $20.0^\circ \mathrm{C}$ will be (Given gas constant $R = 8.3 \quad \mathrm{J} \quad \mathrm{K}^{-1} \quad \mathrm{mol}^{-1}$)

Accepted Answer

$498 \quad \mathrm{J}$

Answer

$249 \quad \mathrm{J}$

Answer

$415 \quad \mathrm{J}$

Answer

$830 \quad \mathrm{J}$