JEE Main 2023 Question Paper (25-Jan-2023) (Shift 1)

Question 1

Electron beam used in an electron microscope, when accelerated by a voltage of $20   \mathrm{kV}$ has a de-Broglie wavelength of ${\lambda}_{0}$. If the voltage is increased to $40  \mathrm{kV}$ then the de-Broglie wavelength associated with the electron beam would be:

Accepted Answer

$ \frac{\lambda_{0}}{\sqrt{2}} $

Answer

$3 \lambda_{0}$

Answer

$9 \lambda_{0}$

Answer

$ \frac{\lambda_0}{2} $

Question 2

An object of mass $8  \mathrm{kg}$ is hanging from one end of a uniform rod $CD$ of mass $2 \mathrm{kg}$ and length $1  \mathrm{m}$, pivoted at its end $C$ on a vertical wall as shown in the figure. It is supported by a cable $AB$ such that the system is in equilibrium. The tension in the cable is:(Take $g = 10  \mathrm{m}  \mathrm{s}^{-2}$)

Accepted Answer

$300 \quad \mathrm{N}$

Answer

$240 \quad \mathrm{N}$

Answer

$90 \quad \mathrm{N}$

Answer

$30 \quad \mathrm{N}$

Question 3

A Carnot engine with efficiency $50\%$ takes heat from a source at $600  \mathrm{K}$. In order to increase the efficiency to $70\%$, keeping the temperature of the sink the same, the new temperature of the source will be:

Accepted Answer

$1000 \quad \mathrm{K}$

Answer

$360 \quad \mathrm{K}$

Answer

$900 \quad \mathrm{K}$

Answer

$300 \quad \mathrm{K}$

Question 4

$T$ is the time period of a simple pendulum on the earth's surface. Its time period becomes $xT$ when taken to a height $R$ (equal to the earth's radius) above the earth's surface. Then, the value of $x$ will be:

Accepted Answer

$2$

Answer

$4$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{4}$

Question 5

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is $ 100 \mathrm{g}$. The time period of the motion of the particle will be (approximately)(take $ g=10  {\mathrm{ms}}^{-2}$, radius of earth $ =6400  \mathrm{km}$)

Accepted Answer

$ 1$ hour $ 24$ minutes

Answer

$ 24$ hours

Answer

$ 1$ hour $ 40$ minutes

Answer

$ 12$ hours