Question

a body of mass m is dropped from a distance r from the centre of the earth of mass m and radius r with the what speed and the body strikes the surface of the earth neglect the air resistance​

Answer 1

Answer:

ANSWER

Since, the initial velocity of body is zero, its total energy is

E=

r

−GmM

....(i)

where, m is the mass of body, M is the mass of the Earth and r its distance from the centre of the Earth. When the body reaches the Earth, let its, velocity be v and its distance from the centre of the Earth equals the Earths radius R. Therefore, the energy is

E=

2

1

mv

2

−

R

GMm

....(ii)

Equating Eqs. (i) and (ii), we get

vv

2

=2GM(

R

1

−

r

1

)

Also, g=

R

2

GM

. Therefore, GM=gR

2

Using this in the above equation, we get

v=R[2g(

R

1

−

r

1

)]

1/2

Now, r=2R (given). Therefore,

v=R[2g(

R

1

−

2R

1

)]

1/2

⇒ Velocity of a body which strike the Earth's surface, v=

gR

.

Explanation:

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