Question

Solve this... plzz guys

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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♦ Given,


Acceleration due to gravity (g) = 9.8 m/s

Radius of Earth (r) = 6.37 × 10^6 m

Gravitational constant (G) = 6.67/10^11 = 6.67 × 10^-11 kgm/s



♦ To find,

Mass of Earth (M)



♦ Now, we know that,

g = GM/r²


=>> gr² = GM

=> gr²/G = M



• Putting the values -


$= \frac{9.8 \times ({6.37 \times 10 }^{6} )^{2} }{6.67 \times {10}^{ - 11} }$


$= \frac{9.8 \times 6.37 \times 6.37 \times {10}^{6} \times {10}^{6} }{6.67 \times {10}^{ - 11} }$


• Using identity : a^m × a^n = a^m+n,

$= \frac{9.8 \times 6.37 \times 6.37 \times 10 ^{12} }{6.67 \times {10}^{ - 11} }$

• Using identity : 1/a^-m = a^m,

$= \frac{9.8 \times 6.37 \times 6.37 \times {10}^{12 } \times {10}^{11} }{6.67}$


$= \frac{9.8 \times 6.37 \times 6.37 \times {10}^{2 3} }{6.67}$


$= \frac{397.65 \times 10 ^{23} }{6.67}$


$= 59.618 \times {10}^{23}$


$= 5.9618 \times {10}^{24}$

= 5.96 × 10^24 kg



♥ •°• The mass of Earth is about 5.96 × 10²⁴ kg.
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Thank you...