JEE Advanced · Physics · 21. EMI

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular
magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in the segments $a b$ and $c d$. Then,

A $I_1>I_2$
B $I_1 < I_2$
C $I_1$ is in the direction ba and $I_2$ is in the direction $c d$
D $I_1$ is in the direction $a b$ and $I_2$ is in the direction $d c$

Verified Solution

Answer & Solution

Correct Answer

(D) $I_1$ is in the direction $a b$ and $I_2$ is in the direction $d c$

Step-by-step Solution

Detailed explanation

Cross $\otimes$ magnetic field passing from the closed loop is increasing. Therefore, from Lenz's law induced current will product $\operatorname{dot} \odot$ magnetic field. Hence, induced current is anticlockwise.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A rod of mass $m$ and length $L,$ pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed $v$ strikes the rod horizontally at a distance $x$ from its pivoted end and gets embedded in it. The combined system now rotates with an angular speed $ω$ about the pivot. The maximum angular speed $ω_{M}$ is achieved for $x = x_{M}$ . Then

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An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II. Match List I with List II and select the correct using answer the code given below the lists :

List - I	List - II
a. $\underset{\quad\quad~~ X }{( C _2 H _5)_3 N}+\underset{ Y }{CH _3 COOH}$	p. Conductivity decreases and then increases
b. $\underset{\quad\quad~~ X }{KI (0.1 M )}+\underset{ Y }{AgNO _3(0.01 M )}$	q. Conductivity decreases and then does not change much
c. $\underset{\text X }{CH _3 COOH}+\underset{\text Y }{KOH}$	r. Conductivity increases and then does not change much
d. $\underset{\text X }{NaOH}+\underset{\text Y }{HI}$	s. Conductivity does not change much and then increases

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Let

f (x) = \sin (π \cos x)

and

g (x) = \cos (2 π \sin x)

be two functions defined for

x > 0 .

Define the following sets whose elements are written in the increasing order:

X = \{x : f (x) = 0\}, Y = \{x : f^{'} (x) = 0\}

Z = \{x : g (x) = 0\}, W = \{x : g^{'} (x) = 0\}

List-

I

contains the sets

X, Y, Z

and

W .

List-

I I

contains some information regarding these sets.

List- $I$	List- $I I$
$(I)$	$X$	$(P)$	$\supseteq \{\frac{π}{2}, \frac{3 π}{2}, 4 π, 7 π\}$
$(I I)$	$Y$	$(Q)$	an arithmetic progression
$(I I I)$	$Z$	$(R)$	NOT an arithmetic progression
$(I V)$	$W$	$(S)$	$\supseteq \{\frac{π}{6}, \frac{7 π}{6}, \frac{13 π}{6}\}$
		$(T)$	$\supseteq \{\frac{π}{3}, \frac{2 π}{3}, π\}$
		$(U)$	$\supseteq \{\frac{π}{6}, \frac{3 π}{4}\}$

Which of the following is the only correct combination?

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An ideal gas of density $ρ = 0.2 kg m^{- 3}$ enters a chimney of height $h$ at the rate of $α = 0.8 kg s^{- 1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_{1} = 0.1 m^{2}$ and the upper end is $A_{2} = 0.4 m^{2}$ . The pressure and the temperature of the gas at the lower end are $600 Pa$ and $300 K$ , respectively, while its temperature at the upper end is $150 K$ . The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g = 10 m s^{- 2}$ and the ratio of specific heats of the gas $γ = 2$ . Ignore atmospheric pressure.

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

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	List I		List II
A.	$θ = 5^{o}$	$P .$	$m_{2} g \sin θ$
B.	$θ = 10^{o}$	$Q .$	$(m_{1} + m_{2}) g \sin θ$
C.	$θ = 15^{o}$	$R .$	$μ m_{2} g \cos θ$
D.	$θ = 20^{o}$	$S .$	$μ (m_{1} + m_{2}) g \cos θ$

List - I	List - II
a. \(\underset{\quad\quad~~ X }{( C _2 H _5)_3 N}+\underset{ Y }{CH _3 COOH}\)	p. Conductivity decreases and then increases
b. \(\underset{\quad\quad~~ X }{KI (0.1 M )}+\underset{ Y }{AgNO _3(0.01 M )}\)	q. Conductivity decreases and then does not change much
c. \(\underset{\text X }{CH _3 COOH}+\underset{\text Y }{KOH}\)	r. Conductivity increases and then does not change much
d. \(\underset{\text X }{NaOH}+\underset{\text Y }{HI}\)	s. Conductivity does not change much and then increases