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 mass of one object is doubled?
What happens to the force between two objects, if the masses of both objects are doubled?
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m.
Answer the following:
You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) (i) a, (ii) b, (iii) c, (iv) 0.
Choose the correct answer from among the given ones:
For the problem 8.10, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii) f, (iv) g.
Can you think of two particles which do not exert gravitational force on each other?
A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m s −1 as it reaches A. The work done by the person on the mass is −3 J. The potential at A is
Let V and E be the gravitational potential and gravitational field at a distance r from the centre of a uniform spherical shell. Consider the following two statements :
(A) The plot of V against r is discontinuous.
(B) The plot of E against r is discontinuous.
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.
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.
Two concentric spherical shells have masses M1, M2 and radii R1, R2 (R1 < R2). What is the force exerted by this system on a particle of mass m1 if it is placed at a distance (R1+ R2)/2 from the centre?
Write an expression for the gravitational force of attraction between two bodies of masses m1 and m2 separated by a distance r.
Multiple Choice Question. Select the correct option.
The mass of earth is 6 × 1024 kg and radius of earth is 6.4 × 106 m. The magnitude of force between the mass of 1 kg and the earth is:
Who stated the law of gravitation?
How will the force of gravitation between two objects change if the distance between them is:
Made four times
Name and state the action and reaction in the following case:
A person walking on the ground.
Two equal and opposite forces acting at the same point on a stationary body. Will the body move? Give reason to explain your answer.
Show that gravity decreases at higher altitudes.
The gravitational force between two bodies is directly proportional to the product of the masses of those bodies and is ______ of the distance between them.
Law of gravitation gives the gravitational force between
Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is
As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would ______.
The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
Give scientific reasons for the following:
Newton's gravitational law is the universal law of gravitation.
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?
For an object outside a uniform solid sphere, from where is the sphere's mass considered to act?
