1
JEE Advanced 2024 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language

A particle of mass $m$ is under the influence of the gravitational field of a body of mass $M(\gg m)$. The particle is moving in a circular orbit of radius $r_0$ with time period $T_0$ around the mass $M$. Then, the particle is subjected to an additional central force, corresponding to the potential energy $V_{\mathrm{c}}(r)=m \alpha / r^3$, where $\alpha$ is a positive constant of suitable dimensions and $r$ is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius $r_0$ in the combined gravitational potential due to $M$ and $V_{\mathrm{c}}(r)$, but with a new time period $T_1$, then $\left(T_1^2-T_0^2\right) / T_1^2$ is given by

[G is the gravitational constant.]

A
$\frac{3 \alpha}{G M r_0^2}$
B
$\frac{\alpha}{2 G M r_0^2}$
C
$\frac{\alpha}{G M r_0^2}$
D
$\frac{2 \alpha}{G M r_0^2}$
2
JEE Advanced 2024 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language
A metal target with atomic number $Z=46$ is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio $r$ of the wavelengths of the $K_\alpha$-line and the cut-off is found to be $r=2$. If the same electron beam bombards another metal target with $Z=41$, the value of $r$ will be
A
2.53
B
1.27
C
2.24
D
1.58
3
JEE Advanced 2024 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_0$, as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity $g$, on two conducting supports at $\mathrm{P}$ and $\mathrm{Q}$. When a current $I$ is passed through the loop, the loop turns about the line $\mathrm{PQ}$ by an angle $\theta$ given by

JEE Advanced 2024 Paper 2 Online Physics - Magnetism Question 3 English
A
$\tan \theta=\pi r I B_0 /(m g)$
B
$\tan \theta=2 \pi r I B_0 /(m g)$
C
$\tan \theta=\pi r I B_0 /(2 m g)$
D
$\tan \theta=m g /\left(\pi r I B_0\right)$
4
JEE Advanced 2024 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

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 $r=10 R$.
JEE Advanced Papers
EXAM MAP