Question

11. Let escape velocity of a body kept at surface of a planet is u. If it is projected at a speed of 200% more than
the escape speed, then its speed in interstellar space will be
(2)
Bu
(3) 2u
(4) 2/2u​

Answer 1

Answer:Escape velocity:12mvesc2=GMmRor, vesc2=2GMR200% more means 3 times the escape velocity, i.e vp=3vescUsing law of conservation of energyor, 12m(vp2− vesc2)=12mvf2or (vp2− vesc2)=vf2or vf=(vp2− vesc2)−−−−−−−−−−√⇒9vesc2−vesc2−−−−−−−−−−√=8√vescvf=8√vesc

Explanation:

Answer 2

The speed in interstellar space is 2√2 u.

Explanation:

Given that,

If it is projected at a speed of 200% more than  the escape speed.

We know that,

Here, the escape velocity is u.

If it is projected at a speed of 200% more than  the escape speed.

$v=v_{e}+200\%v_{e}$

$v=u+\dfrac{200}{100}u$

$v=u+2u$

$v=3u$

We need to calculate the speed in interstellar space

Using formula of speed

$v'=\sqrt{v_{e}^2+v^2}$

$v'=\sqrt{u^2+(3u)^2}$

$v=\sqrt{4u^2}$

$v=2\sqrt{2}u$

Hence, The speed in interstellar space is 2√2 u.

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Topic : escape velocity

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