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 particle of mass m is being rotated on a vertical circle of radius r. If the speed of particle at the highest point be v, then ______________.

(a)

mg=\(\frac{mv^{2}}{r}\)

(b)

mg>\(\frac{mv^{2}}{r}\)

(c)

mg<\(\frac{mv^{2}}{r}\)

(d)

mg≥\(\frac{mv^{2}}{r}\)

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

Two equal masses m₁ and m₂ are moving along the same straight line with velocities 5ms^-1 and -9 ms^-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m₁ and m₂ respectively

(a)

-4 ms^-1 and 10 ms^-1

(b)

10 ms^-1 and 0 ms^-1

(c)

-9 ms^-1 and 5 ms^-1

(d)

5 ms^-1 and 1 ms^-1

If momentum of a body increases by 100% then what will be percentage increase in its kinetic energy?

(a)

200%

(b)

100%

(c)

300%

(d)

400%

In case of negative work, the angle between the force and displacement is ______________.

(a)

0⁰

(b)

90⁰

(c)

45⁰

(d)

180⁰

A force\(\overrightarrow { F } =3\hat { i } +c\hat { j } +2\hat { k } \) acting on a particle causes a displacement \(\overrightarrow { S } =(2\hat { i } -3\hat { j } +4\hat { k } )\) in its own direction. If the work done is 8J, then the value of c is ______________.

(a)

0

(b)

6

(c)

2

(d)

1

Water stored in a dam possesses _______________.

(a)

no energy

(b)

electrical energy

(c)

kinetic energy

(d)

potential energy

An iron sphere of mass 8 kg has the same diameter as a copper sphere of mass 4 kg. Both spheres are dropped simultaneously from a tower. When they are 10 m above the ground, they have the same ____________.

(a)

acceleration

(b)

momenta

(c)

Potential Energy

(d)

Kinetic Energy

How are joule (J) and ergs related _______________.

(a)

1 J = 10⁷ erg

(b)

1 erg = 10^-7 J

(c)

1 J = 10^-7 erg

(d)

none

A bullet is fired and gets embedded in a block kept on table. If table is frictionless, then _____________.

(a)

Kinetic Energy gets conserved

(b)

Potential Energy gets conserved

(c)

Momentum conserved

(d)

both (a) and (c)

A particle of mass m₁ is moving with a velocity v, and another of mass m₂ is moving with velocity v₂ Both of them have the some momentum but their kinetic energies are E₁ and E₂ respectively. If =m₁ > m₂ the ______________.

(a)

E₁2

(b)

\(\frac{E_1}{E_2}=\frac{m_1}{m_2}\)

(c)

E₁>E₂

(d)

E₁=E₂

The potential energy of a system increases if work is done ______________.

(a)

upon the system by a non-conservative force

(b)

upon the system by a conservative force

(c)

By a system against conservative force

(d)

By a system against non conservative force

In an elastic collision

(a)

both momentum and kinetic energy are conserved

(b)

only kinetic energy is conserved

(c)

both momentum and kinetic energy are not conserved

(d)

only momentum is conserved

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water?

(a)

\({{1}\over{2}}{m}{v}^{2}\)

(b)

mv³

(c)

\({{1}\over{2}}{m}{v}^{3}\)

(d)

\({{1}\over{2}}{m}{v}^{2}\)

Which one of the following is not a conservative force?

(a)

Gravitational force

(b)

Electrostatic force between two changes

(c)

Magnetic force, between two magnetic dipoles

(d)

Frictional force

The total work done on a particle is equal to the change in its kinetic energy ______________.

(a)

always

(b)

only if the force acting on the body are conservative

(c)

only in the internal frame

(d)

only if no external force is acting

An object is thrown vertically upwards as it rises its total energy ____________.

(a)

decreases

(b)

increases

(c)

remains constant

(d)

none of the above