A region in the form of an equilateral triangle (in $x-y$ plane) of height $L$ has a uniform magnetic field $\vec{B}$ pointing in the $+z$-direction. A conducting loop $\mathrm{PQR}$, in the form of an equilateral triangle of the same height $L$, is placed in the $x-y$ plane with its vertex $\mathrm{P}$ at $x=0$ in the orientation shown in the figure. At $t=0$, the loop starts entering the region of the magnetic field with a uniform velocity $\vec{v}$ along the $+x$-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
![JEE Advanced 2024 Paper 2 Online Physics - Electromagnetic Induction Question 1 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwpw4d6x/10223706-4d59-4a88-8e49-de89a0b486c2/bfe0db90-1ca9-11ef-a7f1-8b6b33c30c4d/file-6y3zli1lwpw4d6y.png?format=png)
Which of the following graph best depicts the variation of the induced emf $(E)$ in the loop as a function of the distance $(x)$ starting from $x=0$ ?
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 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 2 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwpwitsv/1cb8dbae-90d0-4e58-80a9-b9c6f0f03edf/52096ef0-1cab-11ef-a7f1-8b6b33c30c4d/file-6y3zli1lwpwitsw.png?format=png)