Question

Column $I$ has some statements about the system shown in column $II$, Match appropriate column.

Answer 1

Case(A) Ring will attract the point mass by its gravitational field therefore its kinetic energy will increase first and its potential energy will decrease.
Case(B) Mass m is launched with a velocity greater than $\sqrt{\frac{2GM}{d}}$
where d is the distance between mass M and mass m.
The velocity of mass m will continue decreasing because of gravitational pull due to mass M
Therefore its kinetic energy will decrease on the otherhand system is isolated therefore, its mechanical energy will remain constant and we know that $ME=PE+KE$ therfore its potential energy will increase
Hence statement 1,3 & 4 are correct.
case(C)Density of ball is greater than the density of liquid therefore, the ball will sink down and its velocity will increase so its kinetic energy will increase but due to viscous force its velocity will become constant after its velocity becomes $v=\frac{mg-Upthrust}{6\pi \eta r}$ so KE will become constant.
its potential energy will keep on decreasing.
Hence its mechanical energy will decreases continously. therfore statement 5 is correct.
case(D)Its just a simple system of charge they both will repel each other hence there kinetic energy will increase and potential energy will decrease but overall mechanical energy will remain constant therefore statement 2 & 4 are correct