A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

(a)

\(\sqrt2:1\)

(b)

\(1:\sqrt2\)

(c)

2:1

(d)

1:2

A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

(a)

mv²

(b)

\(\frac{3}{2}\)mv²

(c)

2mv²

(d)

4mv²

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

(a)

\(\sqrt{2gR}\)

(b)

\(\sqrt{3gR}\)

(c)

\(\sqrt{5gR}\)

(d)

\(\sqrt{gR}\)

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

(a)

0.1 %

(b)

0.2 %

(c)

0.4 %

(d)

0.01 %

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

(a)

v

(b)

v²

(c)

v³

(d)

v⁴