JEE Main 2022 Question Paper (26-Jul-2022) (Shift 2)

Question 1

Two projectiles are thrown with the same initial velocity making an angle of $45^\circ$ and $30^\circ$ with the horizontal, respectively. The ratio of their respective ranges will be

Accepted Answer

$2 : \sqrt{3}$

Answer

$1 : \sqrt{2}$

Answer

$ \sqrt{2} : 1 $

Answer

$ \sqrt{3} : 2 $

Question 2

In a Vernier Caliper, 10 divisions of the Vernier scale are equal to 9 divisions of the main scale. When both jaws of the Vernier Caliper touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale, and the 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $1 \mathrm{mm}$. While measuring the diameter of a spherical body, the body is held between two jaws. It is now observed that the zero of the Vernier scale lies between 30 and 31 divisions of the main scale reading, and the 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:

Accepted Answer

$3.10 \mathrm{cm}$

Answer

$3.02 \mathrm{cm}$

Answer

$3.06\mathrm{cm}$

Answer

$3.20 \mathrm{cm}$

Question 3

A ball of mass $0.15 \mathrm{kg}$ hits the wall with its initial speed of $12 \mathrm{m} \mathrm{s}^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $100 \mathrm{N}$, calculate the time duration of the contact of the ball with the wall.

Accepted Answer

$0.036 \mathrm{s}$

Answer

$0.018 \mathrm{s}$

Answer

$0.009 \mathrm{s}$

Answer

$0.072 \mathrm{s}$

Question 4

A body of mass $8 \mathrm{kg}$ and another of mass $2 \mathrm{kg}$ are moving with equal kinetic energy. The ratio of their respective momenta will be

Accepted Answer

$2:1$

Answer

$1:1$

Answer

$1:4$

Answer

$4:1$

Question 5

Two uniformly charged spherical conductors $ A $ and $ B $ of radii $ 5 \mathrm{mm} $ and $ 10 \mathrm{mm} $ are separated by a distance of $ 2 \mathrm{cm} $. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $ A $ and $ B $ will be

Accepted Answer

$2:1$

Answer

$1:2$

Answer

$1:1$

Answer

$1:4$