The velocity with which a body must be thrown vertically upward from the surface of the earth so that it may reach a height of 10R, where R is the radius of the earth and is equal to 6.4×10⁶m is
(Given: Mass of the earth = 6×10²⁴kg)

A. 10.7 ×10⁴m/s

B. 10.7 ×10⁵m/s

C. 1.07 ×10³m/s

D. 1.07 ×10⁴m/s
The relay satellite transmits the television programme continuously from one part to another because its:
(A) Period is greater than the period of rotation of the earth about its axis
(B) Period is less than the period of rotation of the earth about its axis.
(C) Period is equal to the period of rotation of the earth about its axis
(D) Mass is less than the mass of the earth

Formula used: The formula used to solve this question is given by
ω=2π/T,

here ω is the angular velocity of a rotating body

whose period of rotation is equal to T.

Complete step by step solution:
A relay satellite is used for the communication between one place of the earth to the other place. It uses the radio waves which are sent as signals and are received by the antennas located on the earth’s surface. The term “relay” refers to the relay race, where the participating runners pass the baton to the next runner and reach the next leg of the race. Likewise, the signal is transmitted by the relay satellite between the space and the ground. These satellites keep on relaying the signal to each other until the signal finally reaches the ground station.
Now, the relay satellite is a geostationary satellite. We know that a geostationary satellite is a satellite which rotates with an angular velocity equal to the angular velocity of the earth. We know that the angular velocity is related with the time period of rotation by the formula
ω=2π/T
So this means that if the angular velocities are equal, then the time periods of motion must also be equal.
Thus, the time period of a relay satellite is equal to the period of rotation of the earth about its axis.
Hence, the correct answer is option C.

Note:
Not only television programmes, but many types of information are communicated with the help of a relay satellite. For example, in weather forecasting and important defence and intelligence applications, relay satellites are employed.
The tidal waves in the sea are primarily due to:
A.the gravitational effect of the sun on the earth

B.the gravitational effect of the moon on the earth

C. the gravitational effect of the Venus on the earth

D. the atmospheric effect of the earth itself

The tidal waves in the sea are primarily due to the gravitational effect of the moon on the earth.
Four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. The magnitude of gravitational force acting on a particle of mass m placed at the centre of the square will be

(a) (24m²G/a²)

(b) (6m²G/a²)

(c) (4√2Gm²/a²)

(d) Zero
A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the sun are r1 and r2 respectively. The time period of the planet is proportional to
A.(r₁+r₂)^3/2

B.(r₁−r₂)

C.r₁^3/2

D.r₂^3/2
If the angular speed of the earth is increased so much that the objects start flying from the equator, then the length of the day will be nearly.

A. 1 1/2hour
B. 8 hour
C. 18 hour
D. 24 hour
The motion of a planet around sun in an elliptical orbit is shown in the following figure. Sun is situated on one focus. The shaded areas are equal. If the planet takes time t1 and t2 in moving from A to B and from C to D respectively then

(a) t1 > t2

(b) t1 < t2

(c) t1 = t2

(d) information incomplete

Correct option (c) t1 = t2

Explanation: According to Kepler’s second law the line joining the planet to the sun covers equal area in equal time. As shaded areas are equal hence time to cover these areas must also be same. i.e. t1 = t2
Three identical bodies (each mass M) are placed at vertices of an equilateral triangle of arm L, keeping the triangle as such, by what angular speed the bodies should be rotated in their gravitational fields,so that the triangle moves along circumference of circular orbit.
If the distance between earth and the sun were
half of its present value , then how many number of days will be there in at year?
If a graph is plotted between T2 and r3 for a planet, then its slope will be

A.4π²/GM

B.GM/4π²

C.4π GM

D.zero

the value of acceleration due to gravity at the surface of any planet is proportional to

The acceleration due to gravity at the surface of a planet, denoted as g, is given by the formula:

g=GM/R²

where:

G is the gravitational constant,
M is the mass of the planet,
R is the radius of the planet.

From this formula, we can see that g is directly proportional to the mass of the planet (M) and inversely proportional to the square of the radius of the planet (R²).

Therefore, the acceleration due to gravity at the surface of any planet is proportional to:

M/R²

This means:

If the mass of the planet increases while keeping the radius constant, the acceleration due to gravity increases.
If the radius of the planet increases while keeping the mass constant, the acceleration due to gravity decreases.

If the earth were to stop rotating, the value of acceleration due to gravity at Delhi will

A. Increase

B. Decrease

C. Become zero

D. Remain unchanged

Two spheres of same material of radius R′ placed in such a way they are touching to each other is the gravitation force between them is F than:
A. F∝R²

B. F∝R⁴

C. Fα1/R²

D.F∝1/R⁴
Moon is a satellite of the Earth, but weightlessness is not experienced at the surface of the Moon because
A. Its distance from the Earth is more.

B. It is a natural satellite.

C. Its own mass is more.

D. Its size is big but density is very low.

Solution: As Moon has its mass, thus it posses its own gravity (1/6th of that of the Earth). Hence, weightlessness is not experienced at the surface of the Moon.

The correct option is C its own mass is more.
As Moon has its mass, thus it posses its own gravity (1/6th of that of the Earth). Hence, weightlessness is not experienced at the surface of the Moon.
A stone drop from height 'h' reaches to Earth surface in 1sec. If the same stone taken to Moon and drop freely then it will reaches from the surface of the Moon in the time(The 'g' of Moon is 1/6 times of Earth).
A. √6 second

B. 9 second

C. √3 second

D. 6 second
a planet has mass 1/10 of that of earth, while radius is 1/3 that of earth. If a person can throw a stone on earth surface to a height of 90 m, then he will be able to throw the stone on that planet to a height

A**.** 90 m

B**.** 40 m

C**.** 100 m

D**.** 45 m
If the earth stops rotating suddenly, the value of g at any point other than the poles would be
A) decrease
B) constant
C) increase
D) increase or decrease depending on position of earth
A planet revolves in an elliptical orbit around the sun. The semi-major and minor axes are a and b , then the time period is given by :

A. T²∝b³

B. T²∝(a+b/2)³

C. T²∝a³

D. T2∝(a−b/2)³

Solution:

Kepler's Third Law of Planetary Motion states that the square of the orbital period TTT of a planet is directly proportional to the cube of the semi-major axis aaa of its orbit. This law can be mathematically expressed as:

T²∝a³

Therefore, the correct answer is:C. T²∝a³
At some planet 'g' is 1.96m/s2. If it is safe to jump from a height of 2m on earth, then what should be corresponding safe height for jumping on that planet
A. 5m

B. 20m

C. 2m

D. 10m

Gravitation Part 1

The tidal waves in the sea are primarily due to the gravitational effect of the moon on the earth.

Four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. The magnitude of gravitational force acting on a particle of mass m placed at the centre of the square will be

If the angular speed of the earth is increased so much that the objects start flying from the equator, then the length of the day will be nearly.

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Haripriya G

Haripriya G