Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Gravitational field due to 'm1' at a point 'O' is `vec"E"_1 = "Gm"_1/"a"^2 hat"i"`
A negative sign indicates field acting along the negative x-direction
Gravitational field due to 'm2' at a point 'O' is `vec"E"_2 = -"Gm"_2/"a"^2 hat"i"`
Gravitational field due to 'm3' at a point 'O' is `vec"E"_3 = "Gm"_3/"a"^2 hat"j"`
`vec"E" = vec"E"_1 + vec"E"_2 + vec"E"_3`
= `"Gm"_1/"a"^2 hat"i" - "Gm"_2/"a"^2 hat"i" + "Gm"_3/"a"^2 hat"j"`
`vec"E" = "G"/"a"^2 [("m"_1 - "m"_2)hat"i" + "m"_3hat"j"]`
If the masses m1 = m2, then
`vec"E" = "G"/"a"^2 ["m"_3hat"j"]`
APPEARS IN
संबंधित प्रश्न
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 work done by the Sun’s gravitational force on the Earth is __________.
An object of mass 10 kg is hanging on a spring scale which is attached to the roof of a lift. If the lift is in free fall, the reading in the spring scale is ___________.
Will the angular momentum of a planet be conserved? Justify your answer.
What is the difference between gravitational potential and gravitational potential energy?
The work done by Sun on Earth in one year will be
If a comet suddenly hits the Moon and imparts energy which is more than the total energy of the Moon, what will happen?
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.
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.
Earth revolves around the Sun at 30 km s−1. Calculate the kinetic energy of the Earth. In the previous example, you calculated the potential energy of the Earth. What is the total energy of the Earth in that case? Is the total energy positive? Give reasons.
