The linear momentum and position vector of the planet is perpendicular to each other at

(a)

perihelion and aphelion

(b)

at all points

(c)

only at perihelion

(d)

no point

A planet moving along an elliptical orbit is closest to the Sun at distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are linear speeds at these points respectively. Then the ratio \({v_1\over v_2}\) is

(a)

\({r_2\over r_1}\)

(b)

\(({r_2\over r_1})^2\)

(c)

\({r_1\over r_2}\)

(d)

\(({r_1\over r_2})^2\)

The gravitational potential energy of the Moon with respect to Earth is

(a)

always positive

(b)

always negative

(c)

can be positive or negative

(d)

always zero

The work done by the Sun’s gravitational force on the Earth is

(a)

always zero

(b)

always positive

(c)

can be positive or negative

(d)

always negative

An object of mass 10 kg is hanging on a spring scale which is attached to the roof of a lift. If the lift is in free fall, the reading in the spring scale is

(a)

98 N

(b)

zero

(c)

49 N

(d)

9.8 N

The kinetic energy of the satellite orbiting around the Earth is

(a)

equal to potential energy

(b)

less than potential energy

(c)

greater than kinetic energy

(d)

zero

The work done by Sun on Earth in one year will be

(a)

zero

(b)

non-zero

(c)

positive

(d)

negative

Acceleration to Kepler's second law the radius vector of a planet sweeps out equal areas in equal intervals of fire. The law is consequence of conservations of _______________.

(a)

linear momentum

(b)

angular momentum

(c)

energy

(d)

Newton's law of gravitation

 

Two practicals of equal mass m go round a circle of radius R under the action of their mutual gravitational attraction the speed of each particle is ___________.

(a)

\(\frac { 1 }{ 2R } \sqrt { \frac { 1 }{ Gm } } \)

(b)

\(\frac { Gm }{ 2R } \)

(c)

\(\frac { 1 }{ 2 } \sqrt { \frac { GM }{ R } } \)

(d)

\(\sqrt { \frac { 4GM }{ R } } \)

A rocket is fired from the earth. The body is projected the distance between the earth of the moon is r & the mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero, when its from the moon is ______________.

(a)

\(\frac { r }{ 5 } \)

(b)

\(\frac { r }{ 10 } \)

(c)

\(\frac { r }{ 15 } \)

(d)

\(\frac { r }{ 20 } \)

A body of mass m falls from earth's surface at a height equal to twice the radius (R) each. Then the change in P.E of body will be

(a)

2 mgR

(b)

\(\frac { 2 }{ 3 } \) mgR

(c)

3 mgR

(d)

\(\frac { 1 }{ 3 } \) mgR

Starting from the centre of be each having radius R, the variation of g is shown by _____________.

(a)

(b)

(c)

(d)

Let V & E be gravitational potential & gravitational field at a distance r from the centre of a uniform solid sphere, consider the 2 statements
(A) the plot of V against r is discontinuous
(B) the plot of E against r is discontinuous

(a)

both A & B correct

(b)

A is correct but B is wrong

(c)

B is correct but A is wrong

(d)

both A & B wrong

A body is suspended from a spring balance kept in a satellite the reading of the balance is W₁ when the satellite goes in an orbit of radius R and is W₂ when it goes in an orbit of radius 2R

(a)

W₁ = W₂

(b)

W₁2

(c)

W₁>W₂

(d)

W_1≠W₂

A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth the escape speed from the earth is V_e its speed with respect to the satellite________________.

(a)

will be less than V_e

(b)

will be more than V_e

(c)

will be equal to V_e

(d)

will depend on direction of projection

Bernoulli theorem is based on conservation of _____________.

(a)

momentum

(b)

mass

(c)

energy

(d)

angular momentum

A solid floats in a liquid in a partially dipped position ______________.

(a)

The solid exerts a force equal to its weight on the liquid

(b)

The liquid exerts a force of buoyancy on the solid which is equal to the weight of the solid

(c)

The weight of the displaced liquid equals the weight of the solid

(d)

All the above

In a streamline flow ______________.

(a)

the speed ofa particle always remain same

(b)

the velocity of a particle always remains same

(c)

the kinetic energies of all the particles arriving at a given point at the same

(d)

the moments of the particles arriving at a given point are different

When a metal wire is stretched by a load, the fractional change in its volume ΔV/V is proportional to ________________.

(a)

\(\frac { \triangle l }{ l } \)

(b)

\(\left( \frac { \triangle l }{ l } \right) ^{ 2 }\)

(c)

\(\sqrt { \frac { \triangle l }{ l } } \)

(d)

none of these

If two soap bubbles of different radii are connected by a tube, then ____________.

(a)

air flows from bigger to the smaller bubble till the sizes become equal

(b)

air flows from bigger bubble to the smaller bubble till the size are interchanged

(c)

air flows from the smaller bubble to the bigger

(d)

there is number flow of air