JEE Main 2017 Physics Question Paper Set 2 With Solution

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Category: IIT-JEE 2017 Physics Paper 2

Question 1:

Consider an expanding sphere of instantaneous radius 𝑅 whose total mass remains constant. The expansion is such that the instantaneous density 𝜌 remains uniform throughout the volume. The rate of fractional change in density

(\frac{1}{ρ} \frac{d ρ}{d t})

is constant. The velocity 𝑣 of any point on the surface of the expanding sphere is proportional to

A	R	B	$^{}$ $R^{3}$
C	$\frac{1}{R}$	D	$R^{\frac{2}{3}}$

Correct Answer : A

Category: IIT-JEE 2017 Physics Paper 2

Question 2:

Consider regular polygons with number of sides 𝑛 = 3, 4, 5…… as shown in the figure. The center of mass of all the polygons is at height ℎ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is Δ. Then Δ depends on 𝑛 and ℎ as

A	$Δ = h \sin^{2} (\frac{π}{n})$	B	$∆ = h (\frac{1}{\cos (\frac{π}{n})} - 1)$
C	$∆ = h \sin (\frac{2 π}{n})$	D	$∆ = h \tan^{2} (\frac{π}{2 n})$

Correct Answer : B

Category: IIT-JEE 2017 Physics Paper 2

Question 3:

A photoelectric material having work-function 𝜙! is illuminated with light of wavelength

λ (λ ∠ \frac{h c}{\emptyset_{0}})

The fastest photoelectron has a de Broglie wavelength 𝜆!. A change in wavelength of the incident light by Δ𝜆 results in a change Δ𝜆! in 𝜆!. Then the ratio Δ𝜆!/Δ𝜆 is proportional to

A	$\frac{λ_{α}}{λ}$	B	$\frac{λ_{α}^{2}}{λ^{2}}$
C	$\frac{λ_{α}^{3}}{λ}$	D	$\frac{λ_{α}^{3}}{λ^{2}}$

Correct Answer : D

Category: IIT-JEE 2017 Physics Paper 2

Question 4:

A symmetric star shaped conducting wire loop is carrying a steady state current 𝐼 as shown in the figure. The distance between the diametrically opposite vertices of the star is 4𝑎. The magnitude of the magnetic field at the center of the loop is

A	$\frac{μ_{0} I}{4 π a} 6 [\sqrt{3 - 1]}$	B	$\frac{μ_{0} I}{4 π a} 6 [\sqrt{3 + 1}]$
C	$\frac{μ_{0} I}{4 π a} 3 [\sqrt{3 - 1]}$	D	$\frac{μ_{0} I}{4 π a} 3 [2 - \sqrt{3]}$

Correct Answer : A

Category: IIT-JEE 2017 Physics Paper 2

Question 5:

Three vectors 𝑃, 𝑄 and 𝑅 are shown in the figure. Let 𝑆 be any point on the vector 𝑅. The distance between the points 𝑃 and 𝑆 is 𝑏|𝑅|. The general relation among vectors 𝑃, 𝑄 and 𝑆 is

A	$\vec{S} = (1 - b) \vec{p} + b \vec{Q}$	B	$\vec{S} = (b - 1) \vec{p} + b \vec{Q}$
C	$\vec{S} = (1 - b^{2}) \vec{p} + b \vec{Q}$	D	$\vec{S} = (1 - b) \vec{p} + b_{2} \vec{Q}$

Correct Answer : A

Category: IIT-JEE 2017 Physics Paper 2

Question 6:

A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3×10! times heavier than the Earth and is at a distance 2.5×10! times larger than the radius of the Earth. The escape velocity from Earth’s gravitational field is 𝑣! = 11.2 km s!!. The minimum initial velocity (𝑣!) required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)

A	$V_{S} = 22 K m^{s - 1}$	B	$V_{S} = 42 K m^{s - 1}$
C	$V_{S} = 62 K m^{s - 1}$	D	$V_{S} = 72 K m^{s - 1}$

Correct Answer : B

Category: IIT-JEE 2017 Physics Paper 2

Question 7:

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is 𝛿𝑇 = 0.01 seconds and he measures the depth of the well to be 𝐿 = 20 meters. Take the acceleration due to gravity 𝑔 = 10 ms-2 and the velocity of sound is 300 ms-1. Then the fractional error in the measurement, 𝛿𝐿/𝐿, is closest to

A	0.2%	B	1%
C	3%	D	5%

Correct Answer : B

Category: IIT-JEE 2017 Physics Paper 2

Question 8:

A uniform magnetic field 𝐵 exists in the region between 𝑥 = 0 and 𝑥 =

\frac{3 R}{2}

(region 2 in the figure) pointing normally into the plane of the paper. A particle with charge +𝑄 and momentum 𝑝 directed along x-axis enters region 2 from region 1 at point 𝑃! (𝑦 = −𝑅). Which of the following option(s) is/are correct?

A	For 𝐵 > $> \frac{2}{3} \frac{P}{Q R}$ the particle will re-enter region 1	B	For 𝐵 = , $= \frac{8}{13} \frac{P}{Q R}$ the particle will enter region 3 through the point 𝑃 $P_{2}$ on x-axis
C	When the particle re-enters region 1 through the longest possible path in region 2, the magnitude of the change in its linear momentum between point 𝑃 $P_{1}$ and the farthest point from 𝑦-axis is 𝑝/ $\sqrt{2}$	D	For a fixed 𝐵, particles of same charge 𝑄 and same velocity 𝑣, the distance between the point 𝑃 $P_{1}$ and the point of re-entry into region 1 is inversely proportional to the mass of the particle

Correct Answer : A and B

Category: IIT-JEE 2017 Physics Paper 2

Question 9:

The instantaneous voltages at three terminals marked 𝑋, 𝑌 and 𝑍 are given by

v_{x}

v_{0}

sin

v_{y}

v_{0}

sin 𝜔𝑡 +

(w t + \frac{2 π}{3})

and

v_{z}

v_{0}

sin

(w t + \frac{4 π}{3})

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points 𝑋 and 𝑌 and then between 𝑌 and 𝑍. The reading(s) of the voltmeter will be

A	$V_{x y}^{r m s} = v_{0} \sqrt{\frac{3}{2}}$	B	$V_{y z}^{r m s} = v_{0} \sqrt{\frac{1}{2}}$
C	$V_{x y}^{r m s} = v_{0}$	D	independent of the choice of the two terminals

Correct Answer : A and D

Category: IIT-JEE 2017 Physics Paper 2

Question 10:

A point charge +Q is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

A	The electric flux passing through the curved surface of the hemisphere is $- \frac{Q}{2 ε_{0}} (1 - \frac{1}{\sqrt{2}})$	B	Total flux through the curved and the flat surfaces is $\frac{Q}{ε_{0}}$
C	The component of the electric field normal to the flat surface is constant over the surface	D	The circumference of the flat surface is an equipotential

Correct Answer : D and A

Category: IIT-JEE 2017 Physics Paper 2

Question 11:

Two coherent monochromatic point sources

S_{1}

and

S_{2}

of wavelength

λ =

600 nm are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance 𝑑 = 1.8 mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is

∆ θ .

Which of the following options is/are correct?

A	A dark spot will be formed at the point $P_{2}$	B	At $P_{2}$ the order of the fringe will be maximum
C	The total number of fringes produced between $P_{1}$ and $P_{2}$ in the first quadrant is close to 3000	D	The angular separation between two consecutive bright spots decreases as we move from $P_{1}$ to $P_{2}$ along the first quadrant

Correct Answer : B and C

Category: IIT-JEE 2017 Physics Paper 2

Question 12:

A source of constant voltage 𝑉 is connected to a resistance 𝑅 and two ideal inductors

L_{1}

and

L_{2}

through a switch 𝑆 as shown. There is no mutual inductance between the two inductors. The switch 𝑆 is initially open. At 𝑡 = 0, the switch is closed and current begins to flow. Which of the following options is/are correct?

A	After a long time, the current through $L_{1}$ will be $\frac{V}{R} \frac{L_{2}}{R L_{1} + L_{2}}$	B	After a long time, the current through $L_{2}$ will be $\frac{V}{R} \frac{L_{1}}{R L_{1} + L_{2}}$
C	The ratio of the currents through $L_{1}$ and $L_{2}$ is fixed at all times $(t > 0)$	D	At 𝑡 = 0, the current through the resistance 𝑅 is $\frac{V}{R}$

Correct Answer : A,B and C

Category: IIT-JEE 2017 Physics Paper 2

Question 13:

A rigid uniform bar AB of length 𝐿 is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is 𝜃. Which of the following statements about its motion is/are correct?

A	The midpoint of the bar will fall vertically downward	B	The trajectory of the point 𝐴 is a parabola
C	Instantaneous torque about the point in contact with the floor is proportional to sin 𝜃	D	When the bar makes an angle θ with the vertical, the displacement of its midpoint from the initial position is proportional to (1 − cos 𝜃)

Correct Answer : A,C and D

Category: IIT-JEE 2017 Physics Paper 2

Question 14:

Consider a simple 𝑅𝐶 circuit as shown in Figure 1. Process 1: In the circuit the switch 𝑆 is closed at 𝑡 = 0 and the capacitor is fully charged to voltage

v_{0}

(i.e., charging continues for time 𝑇 >> 𝑅𝐶). In the process some dissipation (

E_{D}

) occurs across the resistance 𝑅. The amount of energy finally stored in the fully charged capacitor is

E_{C}

. Process 2: In a different process the voltage is first set to

\frac{V_{0}}{3}

and maintained for a charging time 𝑇 >> 𝑅𝐶. Then the voltage is raised to

\frac{2 V_{0}}{3}

without discharging the capacitor and again maintained for a time 𝑇 >> 𝑅𝐶. The process is repeated one more time by raising the voltage to

V_{0}

and the capacitor is charged to the same final voltage

V_{0}

as in Process 1. These two processes are depicted in Figure 2.

Question; In Process 1, the energy stored in the capacitor

E_{C}

and heat dissipated across resistance

E_{D}

are related by.

A	$E_{C} = E_{D}$	B	$E_{C} = E_{D} I n 2$
C	$E_{C} = \frac{1}{D} E_{D}$	D	$E_{C} = 2 E_{D}$

Correct Answer : A

Category: IIT-JEE 2017 Physics Paper 2

Question 15:

Consider a simple 𝑅𝐶 circuit as shown in Figure 1. Process 1: In the circuit the switch 𝑆 is closed at 𝑡 = 0 and the capacitor is fully charged to voltage

v_{0}

(i.e., charging continues for time 𝑇 >> 𝑅𝐶). In the process some dissipation (

E_{D}

) occurs across the resistance 𝑅. The amount of energy finally stored in the fully charged capacitor is

E_{C}

. Process 2: In a different process the voltage is first set to

\frac{V_{0}}{3}

and maintained for a charging time 𝑇 >> 𝑅𝐶. Then the voltage is raised to

\frac{2 V_{0}}{3}

without discharging the capacitor and again maintained for a time 𝑇 >> 𝑅𝐶. The process is repeated one more time by raising the voltage to

V_{0}

and the capacitor is charged to the same final voltage

V_{0}

as in Process 1. These two processes are depicted in Figure 2.

In Process 2, total energy dissipated across the resistance ED is:

A	$E_{D} = \frac{1}{2} C V_{0}^{2}$	B	$E_{D} = 3 (\frac{1}{2} C V_{0}^{2})$
C	$E_{D} = \frac{1}{3} (\frac{1}{2} C V_{0}^{2})$	D	$E_{D} = C V_{0}^{2}$

Correct Answer : C

Category: IIT-JEE 2017 Physics Paper 2

Question 16:

One twirls a circular ring (of mass 𝑀 and radius 𝑅) near the tip of one’s finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is 𝑟. The finger rotates with an angular velocity

w_{0}

. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is μ and the acceleration due to gravity is 𝑔.

The minimum value of 𝜔! below which the ring will drop down is

A	$\sqrt{\frac{g}{μ (R - r)}}$	B	$\sqrt{\frac{2 g}{μ (R - r)}}$
C	$\sqrt{\frac{3 g}{2 μ (R - r)}}$	D	$\sqrt{\frac{g}{2 μ (R - r)}}$

Correct Answer : A

Category: IIT-JEE 2017 Physics Paper 2

Question 17:

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque 𝜏about an axis normal to the plane of the paper passing through the point 𝑄. Which of the following options is/are correct?

A	If the force is applied at point 𝑃 tangentially then 𝜏 decreases continuously as the wheel climbs	B	If the force is applied normal to the circumference at point 𝑋 then 𝜏 is constant
C	If the force is applied normal to the circumference at point 𝑃 then 𝜏 is zero	D	If the force is applied tangentially at point 𝑆 then 𝜏 ≠ 0 but the wheel never climbs the step

Correct Answer : D

Category: IIT-JEE 2017 Physics Paper 2

Question 18:

w_{0}

The total kinetic energy of the rings is

A	$M w {}_{0}^{2}R^{2}$	B	$\frac{1}{2} M w {}_{0}^{2}{(R - r)}^{2}$
C	$M w {}_{0}^{2}{(R - r)}^{2}$	D	$\frac{3}{2} M w {}_{0}^{2}{(R - r)}^{2}$

Correct Answer : D

JEE Main 2017 Physics Question Paper Set 2 With Solution

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