JEE Advanced Model Paper 9 with solutions for online practice

At any radial distance r, let the speed of the body 1 V conserving total mechanical energy

1

2

mV2 + [−

GMm

r

] = 0 or V = √

2gR2

r

or −

dr

dt

=

(√2g)R

√r

or

−1

R√2g

R

∫

R+n

r1∕2 dr =

t

∫

0

dt or t =

2

3R√2g

[(R+h)3∕2−R3∕2]
Putting = R
t =

1

2

√

2R

g

(2√2 - 1)
R = 6400 km