JEE Main + Advanced ENTHUSIAST COURSE Test Pattern

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Questions and Answers

A charge particle qo is kept at centre of 2 non conducting hemi spherical shell of radius R₁ & R2. If E₁ & E2 is electric field at surfaces of A & B then, what is the correct answer?

E1 ≠ E2 (correct)
E1 = E2
Ratio of flux Φ₁/Φ₂ = 1 (correct)
R1/√R2 = √E2/E1

A ray of light tangentially incident on outer sphere. What is the correct answer?

Ray will never enter inside inner sphere.
Ray is incident tangentially on inner sphere. (correct)
Net deviation suffered by ray is 240°. (correct)
Angle made by ray with normal inside inner sphere is 30°.

Variation of magnification of convex lens vs image distance for real objects is shown. Choose correct statement.

magnitude of intercept on m axis is 1. (correct)
f is equal to intercept of V-axis.
f is equal to slope of graph
f is equal to 1/slope of graph. (correct)

Diagram shows a capacitor connected with a constant current source. Choose the correct option(s) :

the rate of change of voltage across the capacitor in the circuit of figure from top to bottom –166.7 V/s. (A), the capacitor's voltage 10 milliseconds after power is switched on is 1.667V. (C) Signup and view all the answers

A long metallic pipe with internal diameter d is pointing directly downwards. Water is slowly dripping from a nozzle at its lower end, see fig. Water can be considered to be electrically conducting; its surface tension is σ and its density is ρ. A droplet of radius r hangs below the nozzle. The radius grows slowly in time until the droplet separates from the nozzle due to the free fall acceleration g. Always assume that d << r. Choose the correct option(s) :-

Relative to the far-away surroundings, the pipe's electrostatic potential is $. the charge Q of a drop when its radius is r, Q = 4πεοφr (B) Signup and view all the answers

A capacitor consists of two circular parallel plates both with radius R separated by distance d, where d << R, as shown in figure (a). The top plate is connected to a constant voltage source at a potential V while the bottom plate is grounded. Then a thin and small disk of mass m with radius r (<< R, d) and thickness t (<< r) is placed on the center of the bottom plate, as shown in figure (b). Let us assume that the space between the plates is in vacuum with the dielectric constant ɛ0 ; the plates and the disk are made of perfect conductors; and all the electrostatic edge effects may be neglected. The inductance of the whole circuit and the relativistic effects can be safely disregarded. The image charge effect can also be neglected. Choose the correct option(s)

When the disk is placed on the bottom plate, a charge q on the disk of figure (b) is related to the voltage V by q = xV, then x in terms of r, d and ɛo is given by Εοπr²/d (A), The parallel plates lie perpendicular to a uniform gravitational field g. To lift up the disk at rest initially, we need to increase the applied voltage beyond a threshould voltage Vth. The value of Vth is given by √(mgd/x) (B), When the disk is placed on the bottom plate, a charge q on the disk of figure (b) is related to the voltage V by q = xV, then x in terms of r, d and ɛo is given by Εοπr²/d (D) Signup and view all the answers

A massive star of mass M is in uniform circular orbit around a supermassive black hole of mass Mb. Initially, the radius and angular frequency of the orbit are R and @ respectively. According to Einstein's theory of general relativity the space around the two objects is distorted and gravitational waves are radiated. Energy is lost through this radiation and as a result the orbit of the star shrinks gradually. One may assume, however, that the orbit remains circular throughout and Newtonian mechanics holds. Choose the correct option(s) :-

The power radiated through gravitational wave by this star is given by LG = KC*GM2R4ω⁶ where c is the speed of light, G is the universal gravitational constant, and K is a dimensionless constant, then x = -5 & y = 1 (B), An expression for the rate of decrease in the orbital period (dT/dt) in terms of the masses, period T and constants given by dT/dt = 3KG⁵/³M²/³Μ (2π)⁸/³/ C⁵T⁵/³ (C) Signup and view all the answers

An uncharged solid spherical conductor of radius R has its centre at the origin of a cartesian frame OXY Z. Two point charges each of +Q are placed at fixed positions at (5R/2, 0, 0) and (0, 0, 3R/2). There will be induced charges on the sphere due to these charges. Choose the correct option(s)

Electric field at (R/2, R/2, R/2) due to induced charges is given by Ep = 23/2Q/(4πεοR²) (2-2√3)î+(2+√3)ĵ+(9+√3)k (D) Signup and view all the answers

The graph shows variation of flux ($) with time (t) passing through a sphere for varies conditions. Choose the correct option(s) : (Assume : linear charge on x-axis)

Graph 'b' may corresponds to the case when a sphere is moving along x-axis with constant speed and the charge distribution is proportional to x. (A), Graph 'a' may corresponds to the case when a sphere is moving along x-axis with constant speed and the charge distribution is uniform in x-direction. (D) Signup and view all the answers

A non conducting rod AB of length √3R, uniformly distributed charge of linear charge density λ and a non-conducting ring of uniformly distributed charge Q, are placed as shown in the figure. Point A is the centre of ring and line AB is the axis of the ring, perpendicular to plane of ring. The electrostatic interaction energy between ring and rod is:

Qλ/4πε₀(2+√3) (D) Signup and view all the answers

Flashcards

ϕ1/ϕ2 in terms of radii

Ratio of electric flux through two non-conducting hemispherical shells.

Refraction

The bending of light as it passes from one medium to another.