A cosmonaut is circling the earth in a satellite at 7 km/s at a height of 630 km above the surface of earth. Calculate the centripetal force acting on the cosmonaut if his mass is 80 kg (take RE = 6.37 × 106 m )

Question

A cosmonaut is circling the earth in a satellite at 7 km/s at a height of 630 km above the surface of earth. Calculate the centripetal force acting on the cosmonaut if his mass is 80 kg (take RE = 6.37 × 106 m ) (A) zero (B) 560 N (C) 600 N (D) 650 N

Tardigrade Admin · Accepted Answer

The orbital velocity of cosmonaut v0 = 7 km/s = 7000 m/s Radius r = RE + h = (6.37 × 106 + 0.63 × 106) = 7 × 106 m Centripetal force F = (mv2/r) =(80× (7000)2/7× 106) = 560 N

Q. A cosmonaut is circling the earth in a satellite at $7 km / s$ at a height of $630 km$ above the surface of earth. Calculate the centripetal force acting on the cosmonaut if his mass is $80 k g$ (take $R_{E} = 6.37 \times 1 0^{6} m$ )

zero

560 N

600 N

650 N

The orbital velocity of cosmonaut
$v_{0} = 7 km / s = 7000 m / s$
Radius $r = R_{E} + h$
$= (6.37 \times 1 0^{6} + 0.63 \times 1 0^{6})$
$= 7 \times 1 0^{6} m$
Centripetal force
$F = \frac{m v ^{2}}{r}$
$= \frac{80 \times ( 7000 ) ^{2}}{7 \times 1 0 ^{6}}$
$= 560 N$

Q. A cosmonaut is circling the earth in a satellite at 7km/s at a height of 630km above the surface of earth. Calculate the centripetal force acting on the cosmonaut if his mass is 80kg (take RE​=6.37×106m )