Question

if an object is projected from surface of earth with speed v=√6gR then interstellar speed of object ​

Answer 1

Answer:

2√gR.

Explanation:

For getting a velocity in the interstellar, the body when escapes the earth's orbit with the escape velocity which is √(2gR). Where R is the radius of the earth and g is the acceleration due to gravity.

So, the interstellar velocity will be v^2=vc^2 - ve^2 where the vc is the orbital velocity which is given in the question as √(6gR). So, on substituting the values we will get the interstellar velocity of the body when escapes the earth's surface. v=√[6gR - 2gR] which on solving we will get that the velocity will be 2√gR.

Answer 2

Answer:

THE ANSWER TO THE QUESTION IS 2$\sqrt{gR}$

Explanation:

Taking :

g as the acceleration due to gravity

R as the radius of the earth

Let us assume

v denotes interstellar velocity

u denotes orbital velocity

v₁ denoted the projection velocity

Interstellar velocity is the velocity attained by the body when no force is acting on it i.e when it escapes the gravitational attraction of earth

Using the formula for interstellar velocity derived using the energy balance

$v^{2}$=$u^{2}$-$vₓ^{2}$

Calculating

u=$\sqrt{2gR}$

$v^{2}$= 6 gR-2gR

v=2$\sqrt{gR}$

In this manner the answer is obtained.