TS EAMCET 20-July-2022 Shift 1 Solved Paper

Escape speed is v0,
⇒‌‌v0=√‌

2GM

R

.....(i)
Now, if velocity of object at infinity is v, then by conservation of energy we have, Energy at surface = Energy at infinity
‌

−GMm

R

+‌

1

2

m(5v0)2=‌

1

2

mv2+0
Now,
‌

GM

R

=‌

1

2

v02 [from Eq. (i)]
So, ‌‌−‌

1

2

mv02+‌

1

2

m(5v0)2=‌

1

2

mv2
⇒‌‌−v02+25v02=v2
or ‌‌v=√24(v02)
or v=2√6v0