Answer: N=2
Explanation:
We know that at the surface of the earth, value of g=
R
2
GM
At height h above the Earth's surface, the value of acceleration due to gravity g
′
=
(R+h)
2
GM
So it is given that g
′
=
4
g
When the bullet reaches maximum height, acceleration due to gravity is
4
1
th of that at planet's surface.
That implies
4R
2
GM
=
(R+h)
2
GM
→h=R
By conservation of mechanical energy,
R
−GMm
+
2
1
mv
2
=
h+R
−GMm
+0 since velocity is zero at max height. ⇒
2
1
mv
2
=
2R
GMm
v=
R
GM
=
2R
2GM
=
2
1
R
2GM
=
2
1
v
esc
⇒v
esc
=
2
v
⇒N=2
