IIT-JEE Exam

A thin ring of mass 2 kg and radius 0.5 m is rolling without on
a horizontal plane with velocity 1 m/s. A small ball of mass
0.1 kg, moving with velocity 20 m/s in the opposite direction
hits the ring at a height of 0.75 m and goes vertically up with
velocity 10 m/s. Immediately after the collision

(A) the ring has pure rotation about its stationary CM.
(B) the ring comes to a complete stop.
(C) friction between the ring and the ground is to the left.
(D) there is no friction between the ring and the ground.

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IIT-JEE Other Question

Two solid spheres A and B of equal volumes but of different densities dA and
dB are connected by a string. They are fully immersed in a fluid of density dF.
They get arranged into an equilibrium state as shown in the figure with a
tension in the string. The arrangement is possible only if
(A) dA < dF (B) dB > dF
(C) dA > dF (D) dA + dB = 2dF Which of the following statement(s) is/are correct?
(A) If the electric field due to a point charge varies as r-2.5 instead of r-2, then the Gauss law will still be
valid.
(B) The Gauss law can be used to calculate the field distribution around an electric dipole
(C) If the electric field between two point charges is zero somewhere, then the sign of the two charges is
the same.
(D) The work done by the external force in moving a unit positive charge from point A at potential VA to
point B at potential VB is (VB - VA).