Question

with what velocity should a particle be projected so that its height becomes equal to radius of earth

Answer 1

A body is projected up with a velocity equal to 3/4 th of the escape velocityfrom the surface of the earth. The height it reaches is ( Radius of earth is R):

Answer 2

The correct answer to the question is  $\ 112\times 10^2\ m/s$

CALCULATION:

The height of the projectile from the surface of earth is equal to the radius of earth.

Hence, height h = R = $6400\times 10^3\ m$

Here, R is the radius of earth.

At maximum height, the velocity of the projectile is zero.

Hence, the final velocity of the projectile  v = 0.

We are asked to calculate the projected velocity of the particle.

Let the projected velocity is denoted as u .

The particle is a projectile. Hence, the only force that cats on the particle is force of gravity. The acceleration so produced is nothing else than the acceleration due to gravity.

From equation of kinematics, we know that-

                                            $v^2-u^2=\ 2as$

                                       ⇒ $0^2-u^2=\ 2(-g)R$

                                      ⇒  $u^2=\ 2gR$

                                       ⇒ $u=\ \sqrt{2gR}$

                                                  $=\ \sqrt{2\times 9.8\times 6400\times10^{3}}\ m/s$

                                                  $=\ \sqrt{12544\times 10^4}$

                                                  $=\ 112\times 10^2\ m/s$    [ans]