Question

a body of mass m released from height equal to the radius R of the earth. the velocity in which it will strike the earth the earth surface is?

Answer 1

Bonjour!

Question:

A body is released from height equal to the radius of earth the velocity of the object when it strikes the surface is?

Answer:

√

g

R

Explanation:

The potential energy of a mass

m

at a distance


from the center of the earth (assumed to be a spherically symmetric object of mass

M

and radius

R

) is

V

(

r

)

=

−

G

M

m

r

Initially the mass is at rest at

r

=

2

R

. So, its total energy is

V

(

2

R

)

=

−

G

M

m

2

R

Thus, from the law of conservation of energy, its speed

v

when it hits the earth (at

r

=

R

) is given by

1

2

m

v

2

−

G

M

m

R

=

−

G

M

m

2

R

⇒

1

2

m

v

2

=

G

M

m

(

1

R

−

1

2

R

)

=

G

M

m

2

R

⇒

v

2

=

G

M

R

Now, the force on the mass at the surface of the earth is given by

m

g

=

G

M

m

R

2

⇒

g

=

G

M

R

2

Thus

v

2

=

g

R

⇒

v

=

√

g

R