Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
If the masses of the Earth and Sun suddenly double, the gravitational force between them will ___________.
The gravitational potential energy of the Moon with respect to Earth is ____________.
The work done by the Sun’s gravitational force on the Earth is __________.
Will the angular momentum of a planet be conserved? Justify your answer.
Define the gravitational field.
What is meant by the superposition of the gravitational field?
Prove that at points near the surface of the Earth, the gravitational potential energy of the object is U = mgh.
If a comet suddenly hits the Moon and imparts energy which is more than the total energy of the Moon, what will happen?
Calculate the gravitational field at point O due to three masses m1, m2 and m3 whose positions are given by the following figure. If the masses m1 and m2 are equal what is the change in a gravitational field at the point O?
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.
