Advertisements
Advertisements
प्रश्न
Solve the following problem.
Calculate the acceleration due to gravity at a height of 300 km from the surface of the Earth. (M = 5.98 × 1024 kg, R = 6400 km).
Advertisements
उत्तर
Given: h = 300 km = 0.3 × 106 m, M = 5.98 × 1024 kg, R = 6400 km = 6.4 × 106 m, G = 6.67 × 10-11 Nm2/kg2
To find: Acceleration due to gravity at height (gh)
Formula: `"g"_"h" = "GM"/("R + h")^2`
Calculation:
From formula,
`"g"_"h" = (6.67 xx 10^-11 xx 5.98 xx 10^24)/([(6.4 xx 10^6) + (0.3 xx 10^6)]^2)`
`= (6.67 xx 5.98 xx 10^13)/((6.7)^2 xx 10^12)`
= antilog{log(6.67) + log(5.98) - 2log(6.7)} × 10
= antilog{0.8241 + 0.7767 - 2(0.8261)} × 10
= antilog{1.6008 - 1.6522} × 10
= antilog{`bar1`.9486} × 10
= 0.8884 × 10
= 8.884 m/s2
Acceleration due to gravity at 300 km will be 8.884 m/s2.
APPEARS IN
संबंधित प्रश्न
What happens to the force between two objects, if the masses of both objects are doubled?
State Kepler’s law which is represented by the relation r3 ∝ T2.
Can we apply Newton’s third law to the gravitational force ? Explain your answer.
Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?
At noon, the sun and the earth pull the objects on the earth's surface in opposite directions. At midnight, the sun and the earth pull these objects in same direction. Is the weight of an object, as measured by a spring balance on the earth's surface, more at midnight as compared to its weight at noon?
Suppose the gravitational potential due to a small system is k/r2 at a distance r from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?
A person sitting in a chair in a satellite feels weightless because
Inside a uniform spherical shell
(a) the gravitational potential is zero
(b) the gravitational field is zero
(c) the gravitational potential is same everywhere
(d) the gravitational field is same everywhere
Two spherical balls of mass 10 kg each are placed 10 cm apart. Find the gravitational force of attraction between them.
A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the following figure . A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if (a) r < x < 2r, (b) 2r < x < 2R and (c) x > 2R.
A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a (In the following figure). The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P1 and P2 shown in the figure.
How will the force of gravitation between two objects change if the distance between them is:
Halved
How will the force of gravitation between two objects change if the distance between them is:
Doubled
How will the force of gravitation between two objects change if the distance between them is:
Infinite
All objects in the universe attract each other along the line joining their________.
What is meant by the equation :
`g= Gxxm/r^2`
where the symbols have their usual meanings.
A force can produce ________, In an object at rest. It can __________ an object and change its __________ of motion.
What does a force do in the following case?
You twist a piece of rubber.
What does a force do in the following case?
You catch a kicked ball.
You can change the direction in which an object is moving by___________.
Name and state the action and reaction in the following case:
A book lying on a table.
State Newton's law of gravitation. What is the difference between:
g and G?
An apple falls towards the earth due to its gravitational force. The apple also attracts the earth with the same force. Why do we not see the earth rising towards the apple? Explain.
State the universal law of gravitation and derive its mathematical expression.
Shown are several curves (Figure). Explain with reason, which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).
Give scientific reasons for the following:
Newton's gravitational law is the universal law of gravitation.
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If `sqrt8` R is the distance between the centres of a ring (of mass 'm')and a sphere (mass 'M') where both have equal radius 'R'.
Newton's universal law of gravitation applies to ______.
The acceleration of the Moon towards the Earth is approximately ______.
A hollow spherical shell of uniform density exerts what gravitational force on a point mass placed inside it?
