CGPET 2022 Solved Paper

Let M= mass, Re= radius of earth, then
ve=√

2GM

Re

Now, when object is at a height of 7R from earth's surface, let escape speed needed is ve′, then by energy conservation,
PE+KE at separation ' 8R′ from earth's Centre = Total energy at infinity
⇒

−GMm

8Re

+

1

2

m(ve′)2=0
⇒

1

2

m(ve′)2=

GMm

8Re

⇒ve′=

1

2√2

⋅(√

2GM

Re

)
=

1

2√2

⋅ve