Three concentric metallic spherical shells of radii R, 2 R, 3 R are given charges Q_1, Q_2, Q_3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q_1: Q_2: Q_3, is

Three concentric metallic spherical shells of radii R, 2 …

M N

of mass

20 gm

, length

25 cm

and resistance

10 Ω

is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field

B_{0} = 4 T

directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time

t = 0

and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-

I

with an appropriate value from List-

II

, and choose the correct option. [Given: The acceleration due to gravity

g = 10 {ms}^{- 2}

and

e^{- 1} = 0.4

]

	List- $I$		List- $II$
$P$	At $t = 0.2 s$ , the magnitude of the induced emf in Volt	$1$	$0.07$
$Q$	At $t = 0.2 s$ , the magnitude of the magnetic force in Newton	$2$	$0.14$
$R$	At $t = 0.2 s$ , the power dissipated as heat in Watt	$3$	$1.20$
$S$	The magnitude of terminal velocity of the rod in $m s^{- 1}$	$4$	$0.12$
		$5$	$2.00$

JEE Advanced 2023 Hard

A stationary source emits sound of frequency

f_{0} = 492 H z

. The sound is reflected by a large car approaching the source with a speed of

2 m s^{- 1}

. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330

m s^{- 1}

and the car reflects the sound at the frequency it has received).

JEE Advanced 2017 Medium

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1m at

10^{o} C .

Now the end P is maintained at

10^{o} C,

while the end S is heated and maintained at

400^{o} C .

The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is

1.2 \times 10^{- 5} K^{- 1},

the change in length of the wire PQ is

JEE Advanced 2016 Hard

The densities of two solid spheres

A

and

B

of the same radii

R

vary with radial distance

r

as

ρ_{A} (r) = k (\frac{r}{R})

and

ρ_{B} (r) = k {(\frac{r}{R})}^{5}

, respectively, where

k

is a constant. The moments of inertia of the individual spheres about axes passing through their centres are

I_{A}

and

I_{B}

, respectively. If

\frac{I_{B}}{I_{A}} = \frac{n}{10}

, the value of

n

is

JEE Advanced 2015 Hard

A small object is placed at the centre of a large evacuated hollow spherical container. Assume the container is maintained at

0 K

. At time

t = 0

, the temperature of the object is

200 K

. The temperature of the object becomes

100 K

at

t = t_{1}

and

50 K

at

t = t_{2}

. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio

(\frac{t_{2}}{t_{1}})

_________ .

JEE Advanced 2021 Medium

A series $R-C$ combination is connected to an $\mathrm{AC}$ voltage of angular frequency $\omega=500 \mathrm{rad} / \mathrm{s}$. If the impedance of the $R-C$ circuit is $R \sqrt{1.25}$, the time constant (in millisecond) of the circuit is

JEE Advanced 2011 Easy

Column I	Column II
A. \(B _2\)	p. Paramagnetic
B. \(N_2\)	q. Undergoes oxidation
C. \(O _2^{-}\)	r. Undergoes reduction
D. \(O _2\)	s. Bond order
	t. Mixing of 's' and 'p' orbitals

Three concentric metallic spherical shells of radii \(R, 2 R, 3 R\) are given charges \(Q_1, Q_2, Q_3\), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, \(Q_1: Q_2: Q_3\), is

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