1
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as

A
zero
B
mk2r2t2
C
mk2r2t
D
mk2rt
2
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Motion of a particle in x-y plane is described by a set of following equations $$x = 4\sin \left( {{\pi \over 2} - \omega t} \right)\,m$$ and $$y = 4\sin (\omega t)\,m$$. The path of the particle will be :

A
circular
B
helical
C
parabolic
D
elliptical
3
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Match List-I with List-II

List-I List-II
(A) Moment of inertia of solid sphere of radius R about any tangent. (I) $${5 \over 3}M{R^2}$$
(B) Moment of inertia of hollow sphere of radius (R) about any tangent. (II) $${7 \over 5}M{R^2}$$
(C) Moment of inertia of circular ring of radius (R) about its diameter. (III) $${1 \over 4}M{R^2}$$
(D) Moment of inertia of circular disc of radius (R) about any diameter. (IV) $${1 \over 2}M{R^2}$$

Choose the correct answer from the options given below :

A
A - II, B - I, C - IV, D - III
B
A - I, B - II, C - IV, D - III
C
A - II, B - I, C - III, D - IV
D
A - I, B - II, C - III, D - IV
4
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?

A
$$2r_A^2 = r_B^3$$
B
$$r_A^3 = 2r_B^3$$
C
$$r_A^3 = 4r_B^3$$
D
$$T_A^2 - T_B^2 = {{{\pi ^2}} \over {GM}}\left( {r_B^3 - 4r_A^3} \right)$$
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