Physics Part I Chapter 8 Gravitation

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

• 2R

• 

• R/2

• 

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms⁻¹, the escape velocity from the

• 1.1 kms⁻¹

• 11 kms⁻¹

• 110 kms⁻¹

• 0.11 kms⁻¹

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement – I:
For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is 4π GM.
and
Statement – II
If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as 1/r₂, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

• Statement – 1is false, Statement – 2 is true.

• Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

• Statement – 1 is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

• Statement – 1 is true, Statement – 2 is False. 

If g_E and g_m are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the moon/ electronic charge on the earth) to be

• 1

• 0

• g_E/g_M

• g_M/g_E

Average density of the earth

• does not depend on g

• is a complex function of g

• is directly proportional to g

• is inversely proportional to g

The change in the value of g at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of earth, then which one of the following is correct?

• d =h/2

• d=3h/2

• d =2h

• d= h

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between
(you may take G = 6 . 67× 10^-11 Nm²/ kg²)

• 13.34 x 10^-10 J

• 3.33 x 10^-10 J

• 6.67 x10^-9 J

• 6.67 x10^-10 J

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

• moment of inertia

• angular momentum

• angular velocity

• rotational kinetic energy

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

• 

• gx

• 
• 

The time period of an earth satellite in circular orbit is independent of

• the mass of the satellite

• radius of its orbit

• both the mass and radius of the orbit

• neither the mass of the satellite nor the radius of its orbit.

If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

• 2 mgR

• mgR/2

• mgR/4

• mgR

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R around the sun will be proportional to

• 
• 

• Rⁿ

• 

Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen
mh = 1.67 × 10^–27 kg]

• 10^–20 C

• 10^–23 C

• 10^–37 C

• 10^–47 C

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then

• d =1/2 km

• d = 1 km

• d =3/2 km

• d = 2 km

Which of the following statements is correct?
(a) Centre of the mass of a body always coincides with the centre of gravity of the body.
(b) Centre of the mass of a body is the point at which the total gravitational torque on the body is zero
(c) A couple on a body produce both translational and rotational motion in a body.
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

• (b) and (d)

• (a) and (b)

• (b) and (c)

• (c) and (d)

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

• Keep floating at the same distance between them

• Move towards each other

• Move away from each other

• Will become stationary

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

• Raindrops will fall faster

• Walking on the ground would become more difficult

• 'g' on the Earth will not change

• Time period of a simple pendulum on the Earth would decrease

Two 20 g flatworms climb over a very thin wall, 10 cm high. One of the worms is 20 cm long, the other is wider and only 10 cm long. which of the following statement is correct regarding them?

• 20 cm worm has done more work against gravity

• 10 cm worm has done more work against gravity

• Both worms have done equal work against gravity

• Ratio of work done by both the worms is 4:5

A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little less than the amount that is necessary and an auxiliary engine, (only capable of operating for a short time) has to be used as well. When is it best to switch on the auxiliary engine?

• at take-off

• When the rocket has nearly stopped with respect to the Earth

• It doesn't matter

• Can't say

The planets with radii R₁ and R₂ have densities ρ1, ρ2 respectively. Their atmospheric pressure is p1 and p2 respectively. Therefore, the ratio of masses of their atmospheres, neglecting variation of g within the limits of the atmosphere is

• $\frac{{\mathrm{\rho }}_1{\mathrm{R}}_2{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2{\mathrm{R}}_1{\mathrm{\rho }}_2}$

• $\frac{{\mathrm{\rho }}_1{\mathrm{R}}_2{\mathrm{\rho }}_2}{{\mathrm{pP}}_2{\mathrm{R}}_1{\mathrm{\rho }}_1}$

• $\frac{{\mathrm{p}}_1{\mathrm{R}}_1{\mathrm{\rho }}_1}{{\mathrm{p}}_2{\mathrm{R}}_2{\mathrm{\rho }}_2}$

• $\frac{{\mathrm{p}}_1{\mathrm{R}}_1{\mathrm{\rho }}_2}{{\mathrm{p}}_2{\mathrm{R}}_2{\mathrm{\rho }}_1}$

A thin symmertical double convex lens of refractive index μ₂ = 1.5 is placed between a medium of refractive index μ₁ = 1.4 to the left and another medium of refractive index μ₃ = 1.6 to the right. Then, the system behaves as

• a convex lens

• a concave lens

• a glass plate

• a convexo-concave lens

Write the SI unit of Gravitational constant

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to

• $\frac{1}{\mathrm{R}}$

• $\frac{1}{\sqrt{\mathrm{R}}}$

• R

• $\frac{1}{{\mathrm{R}}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

Two planets are revolving around the earth with velocities v₁ and v₂ and in radii r₁ and r₂ ( r₁ > r₂ ) respectively. Then :

• v₁ = v₂

• v₁ > v₂

• v₁ < v₂

• $\frac{{\mathrm{v}}_1}{{\mathrm{r}}_1} =\frac{{\mathrm{v}}_2}{{\mathrm{r}}_2}$

Earth is revolving around the sun. If the distance of the earth from the sun is reduced to 1/4th of the present distance then the length of present day will be reduced by :

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{1}{8}$

• $\frac{1}{6}$

There are two planets and the ratio of radius of the two planets is K but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity ?

• (kg)^1/2

• (kg)^-1/2

• (kg)²

• (kg)^-2

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then

• g' = 3g

• $\mathrm{g}\text{'} = \frac{\mathrm{g}}{9}$

• g' = 9g

• g' = 27g

Two satellites of earth, S₁ and S₂ are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which one of the following statements is true ?

• The time period of S₁ is four times that of S₂

• The potential energies of earth and satellite in the two cases are equal

• S₁ and S₂ are moving with the same speed

• The kinetic energies of the two satellites are equal

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

• 2

• $\frac{1}{2}$

• $\frac{1}{\sqrt{2}}$

• $\sqrt{2}$

A satellite orbiting the earth in a circular orbit of radius R completes one revolution in 3h. If orbital radius of geostationary satellite is 36000 km, orbital radius of earth is

• 6000 km

• 9000 km

• 12000 km

• 15000 km

A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R. If the satellite is intended to move in a circular orbit of radius 7R, the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant= G)

• $\frac{\mathrm{GMm}}{\mathrm{R}}$

• $- \frac{13 \mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

• $\frac{\mathrm{GMm}}{7\mathrm{R}}$

• $-\frac{\mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

The escape velocity for the earth is 11.2 km/s. The mass of another planet 100  times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is

• 280 km/s

• 56.0 km/s

• 112 km/s

• 56 km/s

Change in acceleration due to gravity is same upto a height h from each other the earth surface and below depth x then relation between x and his ( h and x<<<R_e )

• x = h

• x = 2h

• x = $\frac{\mathrm{h}}{2}$

• x = h²

 A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass m and of equal to radius. The centre of the ring is at a distance $\sqrt{3}$a from the centre of the sphere. The gravitational force (Fl exerted by the sphere on the ring is

• $\frac{\sqrt{3} \mathrm{G} \mathrm{Mm}}{8 {\mathrm{a}}^2}$

• $\frac{2 \mathrm{G} \mathrm{M} \mathrm{m}}{3 {\mathrm{a}}^2}$

• $\frac{7 \mathrm{G} \mathrm{Mm}}{\sqrt{2} {\mathrm{a}}^2}$

• $\frac{3 \mathrm{G} \mathrm{Mm}}{{\mathrm{a}}^2}$

A body of mass 2m is placed on earth's surface. Calculate the change in gravitational potential energy, if this body is taken from earth's surface to a height of h, where h = 4R.

• $\frac{2 \mathrm{mgh}}{\mathrm{R}}$

• $\frac{2}{3} \mathrm{mgR}$

• $\frac{8}{5} \mathrm{mgR}$

• $\frac{\mathrm{mgR}}{2}$

A communication satellite of 500 kg revolves around the earth in a circular orbit of radius 4.0 x 10⁷ m in the equatorial plane of the earth from west to east. The magnitude of angular momentum of the satellite is

• ∼ 0.13  × 10¹⁴ kg m² s^-1

• ∼ 1.3  × 10¹⁴ kg m² s^-1

• ∼ 0.58 × 10¹⁴ kg m² s^-1

• ∼ 2.58  × 10¹⁴ kg m² s^-1

The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the earth is ( here R is the radius of the earth )

• $\left(\frac{\mathrm{n}}{\mathrm{n} + 1}\right)$ mgR

• $\left(\frac{\mathrm{n}}{\mathrm{n} - 1}\right)$ mgR

• nmgR

• $\frac{\mathrm{mgR}}{\mathrm{n}}$

Assertion:  Two bodies of masses M and m (M > m) are allowed to fall from the same height if the air resistance for each be the same then both the bodies will reach the earth simultaneously. 

Reason:  For same air resistance, acceleration of both the bodies will be same.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion: Kepler's second law can be understood by conservation of angular momentum principle.

Reason:  Kepler's second law is related with areal velocity which can further be proved to be based on conservation of angular momentum as (dA/dt) = ( r²ω / 2 )

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false

Time period of pendulum, on a satellite orbiting the earth, is

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\pi }$}\right.$

• zero

• $\mathrm{\pi }$

• infinity

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to transfer it from a circular orbit of radius R, to another of radius R₂ (R₂ > R₁ ) is

• GmM $\left(\frac{1}{{\mathrm{R}}_1^2} - \frac{1}{{\mathrm{R}}_2^2}\right)$

• GmM $\left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• 2 GmM $\left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• $\frac{1}{2}$ GmM $\left(\frac{1}{{\mathrm{R}}_1}- \frac{1}{{\mathrm{R}}_2}\right)$

A person is standing in an elevator. In which situation he finds himself weightless?

• Elevator is going up with constant speed.

• Elevator is moving down with constant speed.

• Elevator is accelerating up with g.

• Elevator is accelerating down with g.