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