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
The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?
What happens to the force between two objects, if the distance between the objects is doubled and tripled?
A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2 ×1030 kg, mass of the earth = 6 × 1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 1011 m).
State Kepler’s law which is represented by the relation r3 ∝ T2.
Can two particles be in equilibrium under the action of their mutual gravitational force? Can three particles be? Can one of the three particles be?
The weight of an object is more at the poles than at the equator. Is it beneficial to purchase goods at equator and sell them at the pole? Does it matter whether a spring balance is used or an equal-beam balance is used?
A body is suspended from a spring balance kept in a satellite. The reading of the balance is W1 when the satellite goes in an orbit of radius R and is W2 when it goes in an orbit of radius 2 −R.
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
Consider a planet moving in an elliptical orbit round the sun. The work done on the planet by the gravitational force of the sun
(a) is zero in any small part of the orbit
(b) is zero in some parts of the orbit
(c) is zero in one complete revolution
(d) is zero in no part of the motion.
Four particles of equal masses M move along a circle of radius R under the action of their mutual gravitational attraction. Find the speed of each particle.
Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the centre.
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.
Who stated the law of gravitation?
Distinguish between gravity and gravitation
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:
Made four times
A ball is thrown up with a speed of 4.9 ms-1.
Calculate the maximum height it would gain before it begins to fall.
A ball is thrown up with a speed of 4.9 ms-1.
Prove that the time of ascent is equal to the time of descent.
What does a force do in the following case?
You twist a piece of rubber.
The distance-time values for an object moving along straight line are given below:
| Time (s) | Distance (m) |
| 0 | 0 |
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
Answer the following question.
What are the dimensions of the universal gravitational constant?
What do you mean by a gravitational constant?
Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be ______.
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'.
Observe the figure and answer the questions:
- State Newton's universal law of gravitation.
- If the distance between the two bodies is tripled, how will the gravitational force between them change?
- What will happen to gravitational force, if mass of one of the object is doubled?
If the mass of one object is doubled and distance remains the same, the gravitational force will:
The acceleration of the Moon towards the Earth is approximately:
