1
JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1

On a frictionless horizontal plane, a bob of mass $m=0.1 \mathrm{~kg}$ is attached to a spring with natural length $l_{0}=0.1 \mathrm{~m}$. The spring constant is $k_{1}=0.009 \,\mathrm{Nm}^{-1}$ when the length of the spring $l>l_{0}$ and is $k_{2}=0.016 \,\mathrm{Nm}^{-1}$ when $l < l_{0}$. Initially the bob is released from $l=$ $0.15 \mathrm{~m}$. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is $T=(n \pi) s$, then the integer closest to $n$ is __________.

2
JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1

An object and a concave mirror of focal length $f=10 \mathrm{~cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0}=15 \mathrm{~cm} \mathrm{~s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30 \mathrm{~cm}$, the speed of the mirror $V_{m}$ is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of $V_{m}$ is _________ $\mathrm{cm} \,\mathrm{s}^{-1}$.

3
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_{A}=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_{A}=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_{B}$, the electrostatic charge density varies as $\rho_{B}=$ $\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their SI units.

Which of the following statement(s) is(are) correct?

A
If $r_{B}=\sqrt{\frac{3}{2}}$, then the electric field is zero everywhere outside $B$.
B
If $r_{B}=\frac{3}{2}$, then the electric potential just outside $B$ is $\frac{k}{\epsilon_{0}}$.
C
If $r_{B}=2$, then the total charge of the configuration is $15 \pi k$.
D
If $r_{B}=\frac{5}{2}$, then the magnitude of the electric field just outside $B$ is $\frac{13 \pi k}{\epsilon_{0}}$.
4
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
In Circuit-1 and Circuit- 2 shown in the figures, $R_{1}=1 \,\Omega, R_{2}=2 \,\Omega$ and $R_{3}=3 \,\Omega$.

$P_{1}$ and $P_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are in open conditions, respectively.

$Q_{1}$ and $Q_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are in closed conditions, respectively.

Which of the following statement(s) is(are) correct?
A
When a voltage source of $6 V$ is connected across $\mathrm{A}$ and $\mathrm{B}$ in both circuits, $P_{1} < P_{2}$.
B
When a constant current source of $2 \mathrm{Amp}$ is connected across A and B in both circuits, $P_{1}>P_{2}$.
C
When a voltage source of $6 V$ is connected across $\mathrm{A}$ and $\mathrm{B}$ in Circuit-1, $Q_{1}>P_{1}$.
D
When a constant current source of $2 \mathrm{Amp}$ is connected across A and $\mathrm{B}$ in both circuits, $Q_{2} < Q_{1}$.
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