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?
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
A planet moving along an elliptical orbit is closest to the Sun at distance r1 and farthest away at a distance of r2. If v1 and v2 are linear speeds at these points respectively. Then the ratio `"v"_1/"v"_2` is
What is meant by the superposition of the gravitational field?
Define gravitational potential energy.
Is potential energy the property of a single object? Justify.
Define gravitational potential.
Derive the expression for gravitational potential energy.
The work done by Sun on Earth at any finite interval of time is
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.
