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 ).


pls make it fast pls..........very urgent

Answer 1

Answer:

7.58 × 10²² Kg

Explanation:

a= $\frac{GM}{R^2}$

M= $\frac{aR^2}{G}$ = $\frac{ 1.67 \times (1.74 \times 10^6)^2}{6.67 * 10^{-11}}$ = 7.58 × 10²² Kg

Answer 2

$\red{\large\underline{\underline\mathtt{To\:Find:}}}$

The mass of the "Moon"..

$\blue{\large\underline{\underline\mathtt{Given:}}}$

• Acceleration due to gravity : $1.67ms^{-2}$

• Radius of Moon = $1.74 \times 10^{6}m$

• G = $6.67 \times 10^{-11}$

$\purple{\Large\underline{\underline\mathtt{We\:know:}}}$

☆ We know the relation ,

$\purple{\sf{\boxed{g = \dfrac{GM}{R^{2}}}}}$

☞ Where ,

• g = Acceleration due to gravity

• G = Universal Gravitational constant

• R = Distance

$\red{\Large\underline{\underline\mathtt{Concept:}}}$

From the formula , we can get a exact equation to find out mass of Moon or simply substituting the value in the Formula .........

$\green{\Large\underline{\underline\mathtt{Solution:}}}$

☯ From the relation,

$\purple{\sf{g = \dfrac{GM}{R^{2}}}}$

☯ we get ,

$\purple{\sf{M = \dfrac{gR^{2}}{G}}}$

Substituting the values in it we get,

$\mathtt{\Rightarrow M = \dfrac{\left(1.74 \times 10^{6}\right)^{2} \times 1.67}{6.67 \times 10^{-11}}}$

$\mathtt{\Rightarrow M = \dfrac{1.74 \times 1.74 \times 10^{12} \times 1.67}{6.67 \times 10^{-11}}}$

$\mathtt{\Rightarrow M = \dfrac{5.05 \times 10^{12}}{6.67 \times 10^{-11}}}$

$\mathtt{\Rightarrow M = \dfrac{5.05 \times 10^{23}}{6.67}}$

$\mathtt{\Rightarrow M = \dfrac{\cancel{5.05} \times 10^{23}}{\cancel{6.67}}}$

$\mathtt{\Rightarrow M = 0.75 \times 10^{23}}$

$\mathtt{\Rightarrow M = 7.5 \times 10^{22} kg}$

${\boxed{\therefore Mass = 7.5 \times 10^{22} kg}}$

$\red{\large\underline{\underline\mathtt{Extra\:Information:}}}$

║Some Formulas related to Gravitation║

• Newton's Universal Law of Gravitation

✧ $\mathtt{F = G\dfrac{m_{1}m_{2}}{d^{2}}}$

or,

$\mathtt{G = \dfrac{Fd^{2}}{m_{1}m_{2}}}$

• Equations of motion for free falling body..

✧ $\mathtt{v = u + gt}$

✧$\mathtt{h = ut + \dfrac{1}{2}gt^{2}}$

✧$\mathtt{v^{2} = u^{2} + gh}$

✪ Where,

• v = final velocity
• u = initial velocity
• t = time taken
• g = acceleration due to gravity
• h = height

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