JEE Advanced 2017 — Set 1

A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true? [A] The pressure difference between the leading and trailing faces of the plate is proportional to uv [B] The resistive force experienced by the plate is proportional to v [C] The plate will continue to move with constant non-zero acceleration, at all times [D] At a later time the external force F balances the resistive force Space for rough work Answer for the above question Ans for

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a co-ordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following options is/are correct? [A] The position of the point mass m is: 𝑥= −2 !" !!! [B] The velocity of the point mass m is: 𝑣= !!" !! ! ! [C] The x component of displacement of the center of mass of the block M is: − !" !!! [D] The velocity of the block M is: 𝑉= − ! ! 2𝑔𝑅 Space for rough work Answer for the above question Ans for

A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength λ0 is produced at point O on the rope. The pulse takes time TOA to reach point A. If the wave pulse of wavelength λ0 is produced at point A (Pulse 2) without disturbing the position of M it takes time TAO to reach point O. Which of the following options is/are correct? M O A Pulse 1 Pulse 2 [A] The time TAO = TOA [B] The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope [C] The wavelength of Pulse 1 becomes longer when it reaches point A [D] The velocity of any pulse along the rope is independent of its frequency and wavelength Space for rough work Answer for the above question Ans for

A human body has a surface area of approximately 1 m!. The normal body temperature is 10 K above the surrounding room temperature 𝑇!. Take the room temperature to be 𝑇! = 300 K. For 𝑇! = 300 K, the value of 𝜎𝑇! ! = 460 Wm!! (where 𝜎 is the Stefan- Boltzmann constant). Which of the following options is/are correct? [A] The amount of energy radiated by the body in 1 second is close to 60 Joules [B] If the surrounding temperature reduces by a small amount ∆𝑇! ≪𝑇!, then to maintain the same body temperature the same (living) human being needs to radiate ∆𝑊= 4𝜎𝑇! !∆𝑇! more energy per unit time [C] Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation [D] If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths Space for rough work Answer for the above question Ans for

A circular insulated copper wire loop is twisted to form two loops of area 𝐴 and 2𝐴 as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field 𝐵 points into the plane of the paper. At 𝑡= 0, the loop starts rotating about the common diameter as axis with a constant angular velocity ω in the magnetic field. Which of the following options is/are correct? [A] The emf induced in the loop is proportional to the sum of the areas of the two loops [B] The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone [C] The net emf induced due to both the loops is proportional to cos ωt [D] The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper Space for rough work Answer for the above question Ans for

In the circuit shown, 𝐿= 1 𝜇H, 𝐶= 1 𝜇F and 𝑅= 1 𝑘Ω. They are connected in series with an a.c. source 𝑉= 𝑉! sin 𝜔𝑡 as shown. Which of the following options is/are correct? [A] The current will be in phase with the voltage if 𝜔= 10! rad. s!! [B] The frequency at which the current will be in phase with the voltage is independent of 𝑅 [C] At 𝜔~0 the current flowing through the circuit becomes nearly zero [D] At 𝜔≫10! rad. s!!, the circuit behaves like a capacitor

For an isosceles prism of angle 𝐴 and refractive index µ, it is found that the angle of minimum deviation 𝛿! = 𝐴. Which of the following options is/are correct? [A] For the angle of incidence 𝑖! = 𝐴, the ray inside the prism is parallel to the base of the prism [B] For this prism, the refractive index µ and the angle of prism 𝐴 are related as 𝐴= ! ! cos!! ! ! [C] At minimum deviation, the incident angle 𝑖! and the refracting angle 𝑟! at the first refracting surface are related by 𝑟! = (𝑖!/2) [D] For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is 𝑖! = sin!! sin 𝐴4 cos! ! ! −1 −cos 𝐴 Space for rough work Answers for the above questions V0 sin ω t L = 1 µH C = 1 µF R = 1 kΩ Ans for

A drop of liquid of radius R = 10!! m having surface tension S = !.! !" Nm!! divides itself into 𝐾 identical drops. In this process the total change in the surface energy ∆𝑈= 10!! J. If 𝐾= 10! then the value of α is

An electron in a hydrogen atom undergoes a transition from an orbit with quantum number 𝑛! to another with quantum number 𝑛!. 𝑉! and 𝑉! are respectively the initial and final potential energies of the electron. If !! !! = 6.25, then the smallest possible 𝑛! is Space for rough work Answers for the above questions Ans for

A monochromatic light is travelling in a medium of refractive index 𝑛= 1.6. It enters a stack of glass layers from the bottom side at an angle 𝜃= 30!. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as nm = n – mΔn, where nm is the refractive index of the mth slab and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m – 1)th and mth slabs from the right side of the stack. What is the value of m? Space for rough work Answer for the above question n n - Δn n - 2Δn n - 3Δn n – (m-1)Δn θ 1 2 3 n – mΔn m-1 m ≈ ≈ Ans for