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!