#### The unit of gravitational potential at a distance “r” from a body oThe unit of gravitational potential at a distance “r” from a body of mass “m” in SI system is ____.f mass “m” in SI system is ____.

#### Which of the following statements is true?

“g” is lesser at places at a height above or at depths below the earth’s surface. It is not the same at all the places on the earth. As the equatorial radius is greater than the polar radius of the earth, the value of “g” is greater at the poles than at the equator.

#### Escape speed of a body on the surface of the earth depends on the (i) mass of the body (ii) mass of the earth (iii) radius of the earth.

The escape speed of a body on the surface of the earth depends on the mass of the earth and its radius. It does not depend on the mass of the body.

#### If the rotational speed of the earth increases, then 'G' ____ and 'g' ____.

If the rotational speed of the earth increases, then 'G' remains the same but 'g' decreases. As the rotational speed of the earth increases, the required centripetal force increases, and hence the acceleration due to gravity decreases.

#### 'g' on any planet is directly proportional to ____ of the planet and inversely proportional to ____ of the planet.

Acceleration due to gravity on the surface of a planet is directly proportional to the mass of the planet and is inversely proportional to the square of the radius of the planet.

#### Statement (i): When a body just escapes from a planet, its total energy is negative. Statement (ii): For the body to leave the planet, total energy must be either positive or zero.

For a body to leave a planet, its total energy must be either positive or zero. Hence, when a body just escapes from a planet, its total energy is negative.

#### The work done in moving a body from a position A which is at a height “h_{1}” to a position B which is at a height “h_{2}” from the surface of the earth ____.

Work done in moving a body from position A to another position B which are at two different heights from the surface of the earth depends only on the difference in the heights of the two points from a reference level. Generally, ground is taken as the reference level.

#### Acceleration due to gravity at a point on the surface of the earth is “g”. If the earth shrinks such that its radius reduces to one-third of the present value and its mass remains constant, then acceleration due to gravity at the same point the distance of which does not change from the centre of the earth is ____.

In the first case, g= GM/R^{2}
In the next case even though the radius of the earth reduces to one-third the previous value, distance of the given point from the centre of the earth is still R.
Then, g'=GM/R^{2}=g.

#### Which of the following statements is correct?

Angular momentum of a planet is given by L = mvr, since the angular momentum of a planet is conserved the product "vr" must be constant that means v∝1/r. When the planet is at aphelion, it is at the farthest point from the sun. So, its speed must be least at that point.

#### If the earth is at one fourth of its present distance from the sun, the duration of the year will be ____ of the present year.

Given that R_{2}=R_{1}/4

Since T_{1}^{2}/T_{2}^{2}=R_{1}^{3}/R_{2}^{3}

T_{2}= (R_{2}R_{1})^{3/2}.T_{1}=T_{1}/8

.

#### A geosynchronous satellite has its time period greater than that of a polar satellite. (ii) The orbit of a polar satellite is nearer to the earth when compared to that of the orbit of a geostationary satellite.

The orbit of a polar satellite is closer to the earth than that of a geostationary (geosynchronous) satellite and hence its time period is less than that of the latter.

#### Two identical satellites revolve around the earth in circular orbits or radii in the ratio 1:2. The ratio of their kinetic energies is ____.

The kinetic energy of a satellite orbiting in circular orbits is given by KE=1/2m(GM_{e}/r)
Where ‘r’ is the radius of the orbit.
Here, the mass of the satellites is equal as they are identical. Hence, the kinetic energy of the satellites is inversely proportional to their radii.
Thus, the ratio of their kinetic energies is the inverse ratio of their radii, which is 2:1.

#### T he force by which work done on a body is independent of the path travelled by the body is called ____.

The force by which work done on a body is independent of the path travelled by the body is called conservative force.

#### On the surface of any planet, acceleration due to gravity of a body is independent of ____.

On the surface of planet acceleration due to gravity of a body is independent of mass of the body.

#### Kepler's law of areas is a consequence of ____.

Kepler's law of areas is a consequence of conservation of angular momentum.

#### Two spherical bodies, each of mass 'M' and radius 'R' are in contact with each other. The gravitational attractive force between them is ____.

The distance between their centres of masses is '2R'

The gravitational attractive force

F=GMm/r^{2}=G.M.M/(2R)^{2}
=GM^{2}/4R^{2}.

#### According to Kepler's law of periods, for a planet revolving around the sun, T^{2} ∝ R^{3}. In this expression "R” is ____.

According to Kepler's third law, the square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the elliptical orbit of the planet. The length of the semi major axis is half of the distance between the aphelion and perihelion of the ellipse.

#### Which of the following are true with regards to escape speed of bodies on the surface of the earth?

The escape speed of objects on the surface of any planet depends only on the mass of the planet and its radius. It does not depend on the shape size and volume of the bodies that are projected.

#### Two satellites revolve around the earth at distances 'R_{1}' and 'R_{2}' with frequencies 'n_{1}' and 'n_{2}'respectively, then ____

According to Kepler's Law of periods, T^{2} ∝ R^{3}

But T=1/n, then 1/n^{2}∝R^{3} or n^{2 }R^{3 }= constant that means n_{1}^{2}R_{1}^{3}=n_{2}^{2}R_{2}^{3}

#### In deriving the expression for the escape speed of an object on the surface of a planet we consider the law of conservation of ____.

When a body is projected vertically upwards, its kinetic energy is converted to potential energy. This is the law of conservation of energy and is utilised in deriving the expression for escape speed of a body on the surface of any planet.

#### If gravitation is not a ____ planets wouldn't have obeyed Kepler's law of areas.

A central force is always directed towards or away from a fixed point under such forces; the areal velocity of position vector is constant.

#### The orbital speed of a satellite depends on (i) mass of the planet around which it revolves (ii) mass of the satellite (iii) radius of the planet (iv) altitude of the satellite.

The orbital speed of a satellite depends on the mass of the planet, its radius and the altitude of the satellite. It does not depend on the mass of the satellite.

#### The gravitational potential energy of a body of mass 10 kg at a height 12800 km from the surface of the earth is: (Radius of the earth is 6400 km.)

Given height of the body is 12800 km which is double the radius of the earth. At that height, the value of “g” is not the same as that on the surface of the earth. Thus, we cannot apply the expression “mgh” to find the gravitational potential energy of the body at the given height.

#### The kinetic energy of an orbiting satellite depends on (i) mass of the planet around which it revolves (ii) mass of the satellite(iii) radius of the planet (iv) altitude of the satellite.

The kinetic energy of an orbiting satellite is given by KE=1/2m (GM_{e}/R_{e}+h)

Hence, the kinetic energy of the satellite depends on all the given factors

#### The gravitational force between two masses is independent of ____ the two bodies.

The gravitational force between two masses is independent of state of matter, charge on bodies and the medium between them.

#### The value of escape speed of an object on the surface of the earth is about 11.2 km/s. If the radius of the earth would be increased by eight times without any change in its mass, what would be the value of the escape speed of an object on the surface of the earth?

V_{e}=** √**(2GM_{e})/R_{e }

Given, R’= R + 8R = 9R

Hence, V'_{e}=** √**(2GM_{e})/9R_{e}=1/3** √**(2GM_{e})/R_{e} =1/3V_{e}=11.2/3 = 3.73 km/s

Gravitational potential at a distance “r” from a body of mass “m” in SI system is joule per kilogram (J/kg).

#### If the earth is in the shape of a perfect sphere and of uniform density, the acceleration due to gravity at equator is ____ its value at poles.

If a body is at the equator, it is moving along a circular path of radius 'R'. A part of the gravitational attractive force acts as the required centripetal force and the rest helps the body gain 'acceleration'. If the same body is at poles, total gravitational attractive force helps in accelerating the body. Hence acceleration due to gravity is more at poles than at equator even when the earth is a perfect sphere of uniform density.

#### When two identical masses are placed at a separation of 1 cm, the gravitational attractive force between them is 0.00667 N. Mass of each body is ____.

F=G.Mm/R^{2}

0.00667=6.67×10^{−11}×M^{2}/(0.01)^{2}

Solving for 'M' we get M = 100 kg.

#### The expression “mg(h_{2 }− h_{1})”for change in gravitational potential energy of a body is applicable ____.

The expression “mg(h_{2} − h_{1})” for change in gravitational potential energy of a body is applicable only when h_{2} is much less compared to the earth’s radius. As the point of observation nears to very large altitudes comparable to the radius of the earth, the acceleration due to gravity also changes, due to which the expression becomes invalid.

#### The force of attraction between two unit masses separated by unit distance is known as ____

The force of attraction between two unit masses separated by unit distance is known as universal gravitational constant.

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