Question

Given, the mass of the Earth is 6 x 1024 kg and its radius is 6.4 x 106 m and the value of G is 6.7 x 10-11 N m2 kg-2, what is the force of gravity on a 5 kg mass at the Earth's surface.
1)6.72 x 107 N
2)6.17 x 10-11 N
3)23.2 x 1013 N
4)0.4907 x 102 N

Answer 1

Option (4) 0.4907 × 10² N

Given :-

• Mass of the earth (M) = $\sf{6 \times 10^{24}\: kg}$
• Radius of earth (r) = $\sf{6.4 \times 10^6\: m}$
• Gravitational constant (G) = $\sf{6.7 \times 10^{-11} \:Nm^2kg^{-2}}$
• Mass of object (m) = 5kg

To Find :-

• The force of gravity on a 5 kg mass at the earth's surface.

Solution :-

As we know that,

$\rm \red \bigstar \: F = \frac{GMm}{r^2}$

[ Putting values ]

$\leadsto \sf \: F = \frac{6 . 7 \times 10 {}^{ - 11} \times 6 \times 10 {}^{24} \times 5 }{(6.4 \times 10 {}^{6} ) {}^{2} }$

$\leadsto \sf \: F = \frac{6.7 \times 6 \times 5 \times 10 {}^{ - 11 + 24 } }{4.096 \times 10 {}^{13} }$

$\leadsto \sf \: F = \frac{201 \times 10 {}^{13} }{409.6 \times 10 {}^{11} }$

$\leadsto \sf \: F =0.4907 \times 10 {}^{13 - 11}$

$\leadsto \sf \: F =0.4907 \times 10 {}^{2} \:N \: \: \green \bigstar$

Hence,

• 0.4907 × 10² N force of gravity on a 5 kg mass at the earth's surface.

Answer 2

Explanation:

Given:-

mass of earth=M=6×1024kg

radius=r=6.4×106m

Gravitational constant=G=$6.7×{10}^{-11}N {m}^{2}kg {}^{-2}$

mass of object=m=5kg

To find:-

the force of gravity on the mass of object

Solution :-

As we know that

${:}\longrightarrow$${\boxed {F={\frac {GMm}{{r}^{2}}}}}$

${:}\longrightarrow$$F={\frac {6.7×{10}^{-11}×6×{10}^{24}×5}{{(6.4×106)}^{2}}}$

${:}\longrightarrow$${\frac {6.4×6×5×{10}^{-11+24}}{4.096×{10}^{13}}}$

${:}\longrightarrow$${\frac {201×{10}^{13}}{409.6×{10}^{11}}}$

${:}\longrightarrow$$0.4907×{10}^{13-11}$

${:}\longrightarrow$$0.4907×{10}^{2}Newton$

${:}\longrightarrow$${\underline{\boxed {\bf {F=0.4907×{10}^{2}N}}}}$