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JEE Advanced 2022 Paper 1 Online
Numerical
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A solid sphere of mass $1 \mathrm{~kg}$ and radius $1 \mathrm{~m}$ rolls without slipping on a fixed inclined plane with an angle of inclination $\theta=30^{\circ}$ from the horizontal. Two forces of magnitude $1 \mathrm{~N}$ each, parallel to the incline, act on the sphere, both at distance $r=0.5 \mathrm{~m}$ from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is _________ $m \,s^{-2} .\left(\right.$ Take $g=10\, m s^{-2}$)

JEE Advanced 2022 Paper 1 Online Physics - Rotational Motion Question 20 English

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JEE Advanced 2022 Paper 1 Online
Numerical
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Consider an LC circuit, with inductance $L=0.1 \,\mathrm{H}$ and capacitance $C=10^{-3} \mathrm{~F}$, kept on a plane. The area of the circuit is $1 \mathrm{~m}^{2}$. It is placed in a constant magnetic field of strength $B_{0}$ which is perpendicular to the plane of the circuit. At time $t=0$, the magnetic field strength starts increasing linearly as $B=B_{0}+\beta t$ with $\beta=0.04 \,\mathrm{T\,s}^{-1}$. The maximum magnitude of the current in the circuit is _________ $m A$.
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JEE Advanced 2022 Paper 1 Online
Numerical
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A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$, the range of the projectile is $d$. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is $g^{\prime}=\frac{g}{0.81}$, then the new range is $d^{\prime}=n d$. The value of $n$ is ___________ .

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A medium having dielectric constant $K>1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$, as shown in Figure (a). Now, both the plates are moved by a distance of $\frac{d}{2}$ from their original positions, as shown in Figure (b).

JEE Advanced 2022 Paper 1 Online Physics - Capacitor Question 4 English

In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

A
The electric field inside the dielectric material is reduced by a factor of $2 K$.
B
The capacitance is decreased by a factor of $\frac{1}{K+1}$.
C
The voltage between the capacitor plates is increased by a factor of $(K+1)$.
D
The work done in the process DOES NOT depend on the presence of the dielectric material.
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