Question

On the moon's surface , the acceleration due to gravity is 1.67 m/s^2 . If the radius of the moon is 1.74 * 10^6 m . Calculate the mass ( G = 6.67 * 10^11 Nm^2 / kg^2 ).


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Answer 1

To Find :

• we need to calculate the mass of moon .

Given :

• Acceleration due to gravity = 1.67m/s²
• Radius of moon = 1.74 × 10⁶ m

Gravitational constant G = 6.67 × 10¹¹ Nm²/kg²

Now,

We know that,

$\star \: \huge \pink{ \bf \: M = \frac{gR²}{G}}$

where,

• M = mass of moon
• g = acceleration due to gravity
• R = Radius of moon
• G = Gravitational constant

$\tt \longrightarrow{\large \: M= \frac{1.67 \times (1.74 \times 10 {}^{6} ) {}^{2} }{6.67 \times {10}^{11} }}$

$\tt \longrightarrow{\large \: M = \frac{1.67 \times (1 .74) {}^{2} \times 10 {}^{6 {}^{2} } }{6.67 \times {10}^{ - 11} }}$

$\tt \longrightarrow{\large \: M = \frac{ 1.67\times 3.0276 \times {10}^{12} }{6.67 \times {10}^{ - 11} }}$

$\tt\longrightarrow {\large \: M = \frac{ 5.056092\times {10}^{12 - ( - 11)} }{6.67}}$

$\tt\longrightarrow {\large \: M = \frac{ 5.056092\times {10 {}^{23} }}{6.67}}$

$\tt\longrightarrow {\large \: M = \frac{ 50.56092 \times {10}^{22} }{6.67}}$

$\tt\longrightarrow{\large\: M = 7.5803478261 \times {10}^{22} }$

$\tt \longrightarrow\large \: M = 7.58\times {10}^{22} kg$

Hence,

• Mass of moon is 7.58 × 10²²

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Answer 2

$\mathfrak{\huge{\blue{\underline{Question:-}}}}$

On the moon's surface, the acceleration due to gravity is $\sf 1.67 \: m/s^{2}$. If the radius of the moon is $\sf 7.14 \times 10^{6} \: m$. Calculate the mass.

$\mathfrak{\huge{\blue{\underline{Given:-}}}}$

Acceleration due to gravity = $\sf 1.67 \: m/s^{2}$

Radius of the moon = $\sf 7.14 \times 10^{6} \: m$

$\mathfrak{\huge{\blue{\underline{To \: Find:-}}}}$

The mass of the moon.

$\mathfrak{\huge{\blue{\underline{Solution:-}}}}$

Gravitational constant (G) = $\sf 6.67 \times 10^{-11} \:Nm^{2}/kg^{2}$

Given that,

Acceleration due to gravity = $\sf 1.67 \: m/s^{2}$

Radius of the moon = $\sf 7.14 \times 10^{6} \: m$

∴ Mass of the moon, $\sf M=\dfrac{gR^{2}}{G}$

$\sf M=\dfrac{1.67 \times (1.74 \times 10^{6})^{2}}{6.67 \times 10^{-11}} \: kg$

$\sf = \underline{\underline{7.58 \times 10^{22} \: kg}}$

$\mathfrak{\huge{\blue{\underline{Note:-}}}}$

G = Gravitational constant

g = Acceleration due to gravity

R = Radius of the moon

M = Mass of the moon