1
JEE Advanced 2024 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
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A small electric dipole $\vec{p}_0$, having a moment of inertia $I$ about its center, is kept at a distance $r$ from the center of a spherical shell of radius $R$. The surface charge density $\sigma$ is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle $\theta$ as shown in the figure. While staying at a distance $r$, the dipole is free to rotate about its center.

JEE Advanced 2024 Paper 2 Online Physics - Electrostatics Question 7 English

If released from rest, then which of the following statement(s) is(are) correct?

[ $\varepsilon_0$ is the permittivity of free space.]

A
The dipole will undergo small oscillations at any finite value of $r$.
B
The dipole will undergo small oscillations at any finite value of $r>R$.
C
The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{2 \sigma p_0}{\epsilon_0 I}}$ at $r=2 R$.
D
The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{\sigma p_0}{100 \epsilon_0 I}}$ at $r=10 R$.
2
JEE Advanced 2024 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

A table tennis ball has radius $(3 / 2) \times 10^{-2} \mathrm{~m}$ and mass $(22 / 7) \times 10^{-3} \mathrm{~kg}$. It is slowly pushed down into a swimming pool to a depth of $d=0.7 \mathrm{~m}$ below the water surface and then released from rest. It emerges from the water surface at speed $v$, without getting wet, and rises up to a height $H$. Which of the following option(s) is(are) correct?

[Given: $\pi=22 / 7, g=10 \mathrm{~m} \mathrm{~s}^{-2}$, density of water $=1 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$, viscosity of water $=1 \times 10^{-3} \mathrm{~Pa}$-s.]

A
The work done in pushing the ball to the depth $d$ is $0.077 \mathrm{~J}$.
B
If we neglect the viscous force in water, then the speed $v=7 \mathrm{~m} / \mathrm{s}$.
C
If we neglect the viscous force in water, then the height $H=1.4 \mathrm{~m}$.
D
The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is $500 / 9$.
3
JEE Advanced 2024 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

A positive, singly ionized atom of mass number $A_{\mathrm{M}}$ is accelerated from rest by the voltage $192 \mathrm{~V}$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $\vec{B}_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.

[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} \mathrm{~kg}$, charge of the electron $=1.6 \times 10^{-19} \mathrm{C}$.]

JEE Advanced 2024 Paper 2 Online Physics - Magnetism Question 2 English

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

A
The value of $x$ for $H^{+}$ion is $4 \mathrm{~cm}$.
B
The value of $x$ for an ion with $A_{\mathrm{M}}=144$ is $48 \mathrm{~cm}$.
C
For detecting ions with $1 \leq A_{\mathrm{M}} \leq 196$, the minimum height $\left(x_1-x_0\right)$ of the detector is $55 \mathrm{~cm}$.
D
The minimum width $w$ of the region of the magnetic field for detecting ions with $A_{\mathrm{M}}=196$ is $56 \mathrm{~cm}$.
4
JEE Advanced 2024 Paper 2 Online
Numerical
+4
-0
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The dimensions of a cone are measured using a scale with a least count of $2 \mathrm{~mm}$. The diameter of the base and the height are both measured to be $20.0 \mathrm{~cm}$. The maximum percentage error in the determination of the volume is _______.
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