JEE Advanced 2018 — Set 2

A particle of mass ݉ is initially at rest at the origin. It is subjected to a force and starts moving along the ݔ-axis. Its kinetic energy ܭ changes with time as ݀ܭ/݀ݐ ൌߛݐ, where ߛ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

Consider a thin square plate floating on a viscous liquid in a large tank. The height ݄ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity ݑ଴. Which of the following statements is (are) true?

An infinitely long thin non-conducting wire is parallel to the ݖ-axis and carries a uniform line charge density ߣ. It pierces a thin non-conducting spherical shell of radius ܴ in such a way that the arc ܲܳ subtends an angle 120° at the centre ܱ of the spherical shell, as shown in the figure. The permittivity of free space is ߳଴. Which of the following statements is (are) true?

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length ݂, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

In a radioactive decay chain, Th ଽ଴ ଶଷଶ nucleus decays to Pb ଼ଶ ଶଵଶ nucleus. Let ܰఈ and ܰఉ be the number of ߙ and ߚି particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 ܪݖ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 ܿ݉ and 83.9 ܿ݉. Which of the following statements is (are) true?

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass ݉ൌ0.4 ݇݃ is at rest on this surface. An impulse of 1.0 ܰݏ is applied to the block at time ݐൌ0 so that it starts moving along the ݔ-axis with a velocity ݒሺݐሻൌݒ଴݁ି௧/ఛ, where ݒ଴ is a constant and ߬ൌ4 ݏ. The displacement of the block, in ݉݁ݐݎ݁ݏ, at ݐൌ߬ is __________. Take ݁ିଵൌ0.37.

A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 ݉ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce, in ݉݁ݐݎ݁ݏ, is ___________.

A particle, of mass 10ିଷ݇݃ and charge 1.0 ܥ, is initially at rest. At time ݐൌ0, the particle comes under the influence of an electric field ܧሬԦሺݐሻൌܧ଴sin ߱ݐଓ̂, where ܧ଴ൌ1.0 ܰܥିଵand ߱ൌ10ଷ ݎܽ݀ ݏିଵ. Consider the effect of only the electrical force on the particle. Then the maximum speed, in ݉ ݏିଵ, attained by the particle at subsequent times is ____________.

A moving coil galvanometer has 50 turns and each turn has an area 2 ൈ10ିସ ݉ଶ. The magnetic field produced by the magnet inside the galvanometer is 0.02 ܶ. The torsional constant of the suspension wire is 10ିସ ܰ ݉ ݎܽ݀ିଵ. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 ݎܽ݀. The resistance of the coil of the galvanometer is 50 ߗ. This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 െ1.0 ܣ. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ݋݄݉ݏ, is __________.