Home
Class 11
PHYSICS
A black hole is an object whose gravitat...

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass `=5.98xx10^(24)kg`) have to be compresed to be a black hole?

A

`10^(-9)m`

B

`10^(-6)m`

C

`10^(-2)m`

D

`100 m`

Text Solution

Verified by Experts

The correct Answer is:
C
The earth will become black hole if the escape velocity on earth is equal to the velocity of light,
i.e., `upsilon_(e) = sqrt((2GM)/(R )) = c` or `R = (2GM)/(c^(2))`
`:. R = (2 xx (6.67 xx 10^(-11)) xx (5.98 xx 10^(24)))/((3 xx 10^(8))^(2))`
`= 8.86 xx 10^(-3) m ~~ 10^(-2)m`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Which one of the following is an object with such a strong gravitational field that even light cannot escape from its surface?

Scientists suspect the presence of black hole (a body whose gravitational force is so strong that nothing can escape from its surface (not even light)) in our universe. Find the condition for a uniform spherical body to be a black hole.

Give the order of the following : Mass of earth ( 5.98xx10^(24) kg)

Ratio of the mass of the Earth (5.98xx10^(24)kg) to the average mass of human (60 kg) is

Two stars bound together by gravity orbit othe because of their mutual attraction. Such a pair of stars is referred to as a binary star system. One type of binary system is that of a black hole and a companion star. The black hole is a star that has cullapsed on itself and is so missive that not even light rays can escape its gravitational pull therefore when describing the relative motion of a black hole and companion star, the motion of the black hole can be assumed negligible compared to that of the companion. The orbit of the companion star is either elliptical with the black hole at one of the foci or circular with the black hole at the centre. The gravitational potential energy is given by U=-GmM//r where G is the universal gravitational constant, m is the mass of the companion star, M is the mass of the black hole, and r is the distance between the centre of the companion star and the centre of the black hole. Since the gravitational force is conservative. The companion star and the centre of the black hole, since the gravitational force is conservative the companion star's total mechanical energy is a constant. Because of the periodic nature of of orbit there is a simple relation between the average kinetic energy ltKgt of the companion star Two special points along the orbit are single out by astronomers. Parigee isthe point at which the companion star is closest to the black hole, and apogee is the point at which is the farthest from the black hole. Q. For circular orbits the potential energy of the companion star is constant throughout the orbit. if the radius of the orbit doubles, what is the new value of the velocity of the companion star?

Calculate the angular momentum of earth rotating about its own axis. Take Radius of earth =6.4xx10^(6)m Mass of earth =5.97xx10^(24)kg

Calculate the gravitational force on a body of mass 1 kg lying on the aurface of earth. Given mass of earth. Given mass of earth is 6xx10^(24) kg and radius of earth is 6400 km.

Find the distance of a point from the earth's centre where the resultant gravitational field due to the earth and the moon is zero. The mass of the earth is 6.0xx10^(24)kg and that of the moon is 7.4xx10^(22)kg . The distance between the earth and the moon is 4.0xx10^(5)km .

If earth is taken as a sphere of radius 6400 km and mass 6xx10^(24) kg, what would be the value of g on the surface of earth ?