Advertisements
Advertisements
प्रश्न
Two bodies of masses m and 4m are placed at a distance of r. Calculate the gravitational potential at a point on the line joining them where the gravitational field is zero.
Advertisements
उत्तर
Let the point be the position when the gravitational field is zero.,
`("Gm")/"x"^2 = ("G"(4"m"))/("r" - "x")^2`
`1/"x"^2 = 4/("r" - "x")^2`
Square root on both sides,
`1/"x" = 2/(("r" - "x"))`
∴ x = `"r"/3`
The point P is at a distance `"r"/3` from mass ‘m’ and `"2r"/3` from mass ‘4m’
Gravitational potential V = `(-"Gm")/(("r"/3)) - ("G"(4"m"))/(("2r"/3))`
= `(-3"Gm")/4 - (3"G"(4"m"))/(2"r")`
= `(-3"Gm")/"r" - (12"Gm")/(2"r")`
V = `(-9"Gm")/"r"`
APPEARS IN
संबंधित प्रश्न
If the masses of the Earth and Sun suddenly double, the gravitational force between them will ___________.
If the distance between the Earth and Sun were to be doubled from its present value, the number of days in a year would be ___________.
The magnitude of the Sun’s gravitational field as experienced by Earth is
Will the angular momentum of a planet be conserved? Justify your answer.
Write unit of the gravitational field.
Derive the expression for gravitational potential energy.
Prove that at points near the surface of the Earth, the gravitational potential energy of the object is U = mgh.
The work done by Sun on Earth at any finite interval of time is
If a comet suddenly hits the Moon and imparts energy which is more than the total energy of the Moon, what will happen?
What is the gravitational potential energy of the Earth and Sun? The Earth to Sun distance is around 150 million km. The mass of the Earth is 5.9 × 1024 kg and the mass of the Sun is 1.9 × 1030 kg.
