The mass of the earth is 6.00 x 1024 kg and that of the moon is 7.40× 1022kg. The constant of gravitation G=6.67× 10-11 N-m2/kg2. The potential energy of the system is -7.79× 1023 J. The mean distance between the earth and moon is

Question

The mass of the earth is 6.00 x 1024 kg and that of the moon is 7.40× 1022kg. The constant of gravitation G=6.67× 10-11 N-m2/kg2. The potential energy of the system is -7.79× 1023 J. The mean distance between the earth and moon is (A)  ~3.80× 108m  (B)  ~3.37× 106m  (C)  ~7.60× 104 text m  (D)  ~1.90× 102 text m

Tardigrade Admin · Accepted Answer

U=(GMm/r) ⇒ 7.79× 1028 =(6.67× 10-11× 7.4× 1022× 6× 1024/r) ⇒ r=3.8× 108 m

Q. The mass of the earth is 6.00 x 1024 kg and that of the moon is $7.40 \times 10^{22} k g .$ The constant of gravitation $G = 6.67 \times 10^{- 11} N - m^{2} / k g^{2} .$ The potential energy of the system is $- 7.79 \times 10^{23} J .$ The mean distance between the earth and moon is

$3.80 \times 10^{8} m$

$3.37 \times 10^{6} m$

$7.60 \times 10^{4} m$

$1.90 \times 10^{2} m$

$U = \frac{GM m}{r}$
$\Rightarrow$ $7.79 \times 10^{28}$
$= \frac{6.67 \times 10 ^{- 11} \times 7.4 \times 10 ^{22} \times 6 \times 10 ^{24}}{r}$
$\Rightarrow$ $r = 3.8 \times 10^{8} m$

Q. The mass of the earth is 6.00 x 1024 kg and that of the moon is 7.40×1022kg. The constant of gravitation G=6.67×10−11N−m2/kg2. The potential energy of the system is −7.79×1023J. The mean distance between the earth and moon is

3.80×108m

3.37×106m

7.60×104m

1.90×102m