JEE Main 2022 Question Paper (27-Jun-2022) (Shift 2)

Question 1

The SI unit of a physical quantity is $\mathrm{Pascal}	ext{-}\mathrm{sec}$. The dimensional formula of this quantity will be

Accepted Answer

$ M L^{-1} T^{-1} $

Answer

$ML^{2}T^{-1}$

Answer

$M^{-1}L^{3}T^{0}$

Answer

$ M L^{-1} T^{-2} $

Question 2

The distance of the Sun from Earth is $1.5 \times 10^{11} \, \mathrm{m}$ and its angular diameter is $2000''$ when observed from the Earth. The diameter of the Sun will be

Accepted Answer

$1.45 	imes 10^{9} \quad \mathrm{m}$

Answer

$2.45 	imes 10^{10} \quad \mathrm{m}$

Answer

$1.45 	imes 10^{10} \quad \mathrm{m}$

Answer

$0.14 	imes 10^{9} \quad \mathrm{m}$

Question 3

When a ball is dropped into a lake from a height $4.9 \ \mathrm{m}$ above the water level, it hits the water with a velocity $v$ and then sinks to the bottom with the constant velocity $v$. It reaches the bottom of the lake $4.0 \ \mathrm{s}$ after it is dropped. The approximate depth of the lake is

Accepted Answer

$29.4 \quad \mathrm{m}$

Answer

$39.2 \quad \mathrm{m}$

Answer

$19.6 \quad \mathrm{m}$

Answer

$73.5 \quad \mathrm{m}$

Question 4

One end of a massless spring of spring constant $k$ and natural length $l_0$ is fixed while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through the fixed end, then the elongation of the spring will be

Accepted Answer

$\frac{m \omega^{2} l_{0}}{k - m \omega^{2}}$

Answer

$\frac{k - m \omega^{2} l_{0}}{m \omega^{2}}$

Answer

$\frac{m \omega^{2} l_{0}}{k + m \omega^{2}}$

Answer

$\frac{k + m \omega^{2} l_{0}}{m \omega^{2}}$

Question 5

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt{x\left(u^{2} - gL\right)}$. The value of $x$ is

Accepted Answer

$2$

Answer

$3$

Answer

$4$

Answer

$1$