JEE Advanced 2017 — Set 2

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 ! ! !" !" is constant. The velocity 𝑣 of any point on the surface of the expanding sphere is proportional to [A] 𝑅 [B] 𝑅! [C] ! ! [D] 𝑅!/! Space for rough work Answer for the above question Ans for

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 ∆. Then ∆ depends on 𝑛 and ℎ as h h h [A] ∆= ℎ sin! ! ! [B] ∆= ℎ ! !"# ! ! −1 [C] ∆= ℎsin !! ! [D] ∆= ℎtan! ! !! Space for rough work Answer for the above question Ans for

A photoelectric material having work-function 𝜙! is illuminated with light of wavelength 𝜆 𝜆< !! !! . The fastest photoelectron has a de Broglie wavelength 𝜆!. A change in wavelength of the incident light by ∆𝜆 results in a change ∆𝜆! in 𝜆!. Then the ratio ∆𝜆!/∆𝜆 is proportional to [A] 𝜆!/𝜆 [B] 𝜆! !/𝜆! [C] 𝜆! !/𝜆 [D] 𝜆! !/𝜆!

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 I 4a [A] !!! !!" 6[ 3 −1] [B] !!! !!" 6[ 3 + 1] [C] !!! !!" 3[ 3 −1] [D] !!! !!" 3[2 − 3] Space for rough work Answers for the above questions Ans for

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] 𝑆= 1 −𝑏𝑃+ 𝑏𝑄 [B] 𝑆= (𝑏−1)𝑃+ 𝑏𝑄 [C] 𝑆= 1 −𝑏! 𝑃+ 𝑏𝑄 [D] 𝑆= 1 −𝑏𝑃+ 𝑏!𝑄 Space for rough work Answer for the above question Ans for

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! = 22 km s!! [B] 𝑣! = 42 km s!! [C] 𝑣! = 62 km s!! [D] 𝑣! = 72 km s!!

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% Space for rough work Answers for the above questions Ans for

A uniform magnetic field 𝐵 exists in the region between 𝑥= 0 and 𝑥= !! ! (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? × × × × × × × × × × × × × × × × × × × × × × × × × × × P1 P2 Region 1 Region 2 Region 3 3R/2 O y (y = -R) +Q B x [A] For 𝐵> ! ! ! !" , the particle will re-enter region 1 [B] For 𝐵= ! !" ! !" , the particle will enter region 3 through the point 𝑃! 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! and the farthest point from 𝑦-axis is 𝑝/ 2 [D] For a fixed 𝐵, particles of same charge 𝑄 and same velocity 𝑣, the distance between the point 𝑃! and the point of re-entry into region 1 is inversely proportional to the mass of the particle Space for rough work Answer for the above question Ans for

The instantaneous voltages at three terminals marked 𝑋, 𝑌 and 𝑍 are given by 𝑉! = 𝑉! sin 𝜔𝑡, 𝑉! = 𝑉! sin 𝜔𝑡+ !! ! and 𝑉! = 𝑉! sin 𝜔𝑡+ 4𝜋 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!" !"# = 𝑉! ! ! [B] 𝑉!" !"# = 𝑉! ! ! [C] 𝑉!" !"# = 𝑉! [D] independent of the choice of the two terminals

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 − ! !!! 1 − ! ! [B] Total flux through the curved and the flat surfaces is ! !! [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 Space for rough work Answers for the above questions Ans for