Question

If the satellite is stopped suddenly in its orbit whichis at a distance radius of earth from earth's surface and allowed to fall freely into the earth. The speed with which it hits the surface of earth will be.

• A.
  1. $7.919m/s$
     
• B. $7.919km/s$
• C. $11.2m/s$
• D. $11.2km/s$

Answer 1

Answer: (B)

$7.919km/s$

At $h=R,$ K.E is zero as satellite is stopped suddenly.

$T.E_h=0+(-\frac{GMm}{2R})$ $(r=h+R=2R)$

At the surface of earth, let velocity attained be v.

$T.E_s=\frac{1}{2}m{v}^2+(-\frac{GMm}{R})$

Apply conservation of energy at h and surface of earth-

$-\frac{GMm}{2R}=\frac{1}{2}m{v}^2-\frac{GMm}{R}$

$⟹v=\sqrt{\frac{GM}{R}}$

$v=\sqrt{gR}$ (using $GM=g{R}^2$)

$v=\sqrt{9.8\times 6400\times 1000}$

$⟹v=7.919km/s$