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Question: The mass of the earth is\(= 6.67 \times 10 ^ { - 11 } \mathrm {~N} \mathrm {~m} ^ { 2 } \mathrm {~kg...

The mass of the earth is=6.67×10−11 N m2 kg−2= 6.67 \times 10 ^ { - 11 } \mathrm {~N} \mathrm {~m} ^ { 2 } \mathrm {~kg} ^ { - 2 })

A

3.8×108 m3.8 \times 10 ^ { 8 } \mathrm {~m}

B

3.37×106 m3.37 \times 10 ^ { 6 } \mathrm {~m}

C

7.60×104 m7.60 \times 10 ^ { 4 } \mathrm {~m}

D

1.9×102 m1.9 \times 10 ^ { 2 } \mathrm {~m}

Answer

3.37×106 m3.37 \times 10 ^ { 6 } \mathrm {~m}

Explanation

Solution

Here, Potential energy of system,

Mass of earth,

Mass of the moon,

MM=7.4×1022 kg\mathrm { M } _ { \mathrm { M } } = 7.4 \times 10 ^ { 22 } \mathrm {~kg}

The potential energy of the earth – moon system is

Where r is the mean distance between earth and

moon.

∴r=−GMEMMU\therefore \mathrm { r } = - \frac { \mathrm { GM } _ { \mathrm { E } } \mathrm { M } _ { \mathrm { M } } } { \mathrm { U } }

=−6.67×10−11×6×1024×7.4×1022−7.79×1028= - \frac { 6.67 \times 10 ^ { - 11 } \times 6 \times 10 ^ { 24 } \times 7.4 \times 10 ^ { 22 } } { - 7.79 \times 10 ^ { 28 } }

=3.8×108 m= 3.8 \times 10 ^ { 8 } \mathrm {~m}