Question

A satellite revolves around the earth in a circular
orbit of radius 6400 km and completes one
revolution in 84 minutes. Calculate its linear speed
in m/s.​

Answer 1

V=(2×22/7×6400)÷84/60

V=28734.6km/hr

Answer 2

${ \bf{ \underline{ \red{ \underline{ \red{ Question: - }}}} }}</p><p>$

A satellite revolves around the earth in a circular orbit of radius 6400 km and completes one revolution in 84 minutes. Calculate its linear speed in m/s. ?

${ \bf{ \underline{ \red{ \underline{ \red{ Solution: - }}}} }}$

Here,

6400 Km = 6400 × 10³ m ..... ( 1 )

84 minutes = 5040 sec ..... ( 2 )

Radius of circular orbit around earth

= 6400 × 10³ Km { from ( 1 )}

Tame taken by satellite to complete revolution = 5040 sec { from ( 2 )}

We Know formula of circumference of circle = 2πr { length of circular orbit }

${ \bf{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: \frac{2 \pi \: r}{Time} }}}}}}$

${ \bf{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: \frac{2 \pi \: r}{5040} }}}}}}$

${ \bf{ \small{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: \frac{2 \times { \frac{22}{7} } \times \: 6400 \times {10}^{3} }{5040} }}}}}}}$

${ \bf{ \small{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: \frac{{ \frac{44}{7} } \times \: 6400 \times {10}^{3} }{5040} }}}}}}}$

${ \bf{ \small{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: \frac{ { \frac{281600}{7} } \times {10}^{3} }{5040} }}}}}}}$

${ \bf{ \small{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: \frac{281600}{7 \times 5040} \times {10}^{3} }}}}}}}$

${ \bf{ \small{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: \frac{281600}{352580} \times {10}^{3} }}}}}}}$

${ \bf{ \small{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: 0.79868 \times {10}^{3} }}}}}}}$

${ \bf{ \small{ \small{ \red{ \dashrightarrow{ \gray{Linear \: speed \: = \: 798.68 \: m/s \: (approx) }}}}}}}$

Hence linear speed of satellite is

798.68 m/s

i hope it helpa you.