Advertisements
Advertisements
Question
A body weighs 5.6 kg wt on the surface of the Earth. How much will be its weight on a planet whose mass is 7 times the mass of the Earth and radius twice that of the Earth’s radius?
Advertisements
Solution
Given:
- Force/weight of the body on earth = 5.6 kg wt
- Mass of the planet = 7 × Mass of Earth
- Radius of the planet = 2 times Radius of the Earth
To find: Weight of the body on the surface of the planet
Calculation:
Let the mass of Earth be 'm' kg.
Let the distance between the two bodies be 'r' m.
F = G`("m" " m"_2)/"r"^2` ...(i)
Force of Gravitation between the two bodies when mass of Earth is 7 times and the distance is doubled.
F' = G`(7 "m m"_2)/(2"r")^2`
F' = G`(7 "m m"_2)/(4"r"^2)` ...(ii)
Now, dividing Equation (i) from Equation (ii), we get:
`=> ("F'")/"F" = (cancel"G"(7 "m m"_2)/(4"r"^2))/(cancel"G"("m m"_2)/"r"^2`
`=> "F'"/"F" = (7 "m m"_2)/(4"r"^2) xx "r"^2/"m m"_2`
`=> "F'"/"F" = (7 cancel("m m"_2))/(4cancel("r"^2)) xx cancel("r"^2)/cancel("m m"_2)`
`=> "F'"/"F" = 7/4`
Now, by substituting the value of F in the Equation, we get:
`=> "F'"/5.6 = 7/4`
`=> "F'" = 7/4 xx 5.6`
`=> "F'" = 7 xx 1.4`
⇒ F' = 9.8 kg wt
APPEARS IN
RELATED QUESTIONS
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.
At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0. (a) Find the speed of the ship due to rotation of the earth about its axis. (b) Find the difference between T0 and the earth's attraction on the bob. (c) If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is ω and radius of the earth is R.
The radius of a planet is R1 and a satellite revolves round it in a circle of radius R2. The time period of revolution is T. Find the acceleration due to the gravitation of the planet at its surface.
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
Choose the correct option.
The binding energy of a satellite revolving around the planet in a circular orbit is 3 × 109 J. It's kinetic energy is ______.
Answer the following question in detail.
Why an astronaut in an orbiting satellite has a feeling of weightlessness?
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
Calculate the kinetic energy, potential energy, total energy and binding energy of an artificial satellite of mass 2000 kg orbiting at a height of 3600 km above the surface of the Earth.
Given: G = 6.67 × 10-11 Nm2/kg2
R = 6400 km, M = 6 × 1024 kg
Solve the following problem.
Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.
(ME = 5.98 × 1024 kg, R = 6.4 × 106 m)
The ratio of energy required to raise a satellite of mass 'm' to a height 'h' above the earth's surface of that required to put it into the orbit at same height is ______.
[R = radius of the earth]
Two satellites of a planet have periods of 32 days and 256 days. If the radius of the orbit of the former is R, the orbital radius of the Latter is ______
The kinetic energy of a revolving satellite (mass m) at a height equal to thrice the radius of the earth (R) is ______.
There is no atmosphere on moon because ____________.
An aircraft is moving with uniform velocity 150 m/s in the space. If all the forces acting on it are balanced, then it will ______.
If a body weighing 40 kg is taken inside the earth to a depth to radius of the earth, then `1/8`th the weight of the body at that point is ______.
A geostationary satellite is orbiting the earth at the height of 6R above the surface of earth. R being radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth is ____________.
If a body weighing 40 kg-wt is taken inside the earth to a depth to `1/2` th radius of the earth, then the weight of the body at that point is ____________.
A satellite of mass 'm' is revolving around the earth of mass 'M' in an orbit of radius 'r' with constant angular velocity 'ω'. The angular momentum of the satellite is ______.
(G =gravitational constant)
A satellite is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is ______ (R = radius of the earth).
A satellite revolves around a planet very close to its surface. By what maximum factor can its kinetic energy be increased suddenly, such that it revolves in orbit in the same way?
What is the approximate period of revolution for the Moon, Earth's only natural satellite?
What is the typical altitude range for a polar satellite's orbit?
Which of the following is an example of a communication (geostationary) satellite launched by India?
