JEE Main 2022 Question Paper (26-Jun-2022) (Shift 1)

Question 1

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

Accepted Answer

$\left[\mathrm{MLT}^{-2}\right]$

Answer

$\left[\mathrm{M}^0 \mathrm{L}^{-1} \mathrm{T}^0\right]$

Answer

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

Answer

$\left[\mathrm{ML}^2\mathrm{T}^{-2}\right]$

Question 2

A person is standing in an elevator. In which situation does he experience weight loss?

Accepted Answer

When the elevator moves downward with constant acceleration

Answer

When the elevator moves upward with constant acceleration

Answer

When the elevator moves upward with uniform velocity

Answer

When the elevator moves downward with uniform velocity

Question 3

An object is thrown vertically upwards. At its maximum height, which of the following quantities becomes zero?

Accepted Answer

Momentum

Answer

Potential energy

Answer

Acceleration

Answer

Force

Question 4

A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in the figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$, while the angular position of point $Q$ is $\alpha$ with respect to point $P$. Which of the following graphs represents the correct relation between $A$ and $\alpha$ when the ball moves from $Q$ to $R$?

Accepted Answer

""

Answer

Answer

Answer

Question 5

A thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2 \mathrm{rad} \mathrm{s}^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity (in $\mathrm{rad} \mathrm{s}^{-1}$).

Accepted Answer

$\frac{2M}{\left(M + 2m\right)}$

Answer

$\frac{M}{\left(M + m\right)}$

Answer

$\frac{(M + 2m)}{2M}$

Answer

$\frac{2\left(M+2m\right)}{M}$