Question

find out the weight of an object on moon. mass of earth - 5.98 x10²⁴ , moon - 7.36 × 10²² ... Radius of earth = 6.37× 10⁶ .. moon = 1.74 × 10⁶

No spam please ​

Answer 1

Explanation:

Hey!

Given=mass of moon=7.36×10^22

mass of earth=6.37×10^24

radius of moon=1.74×10^6

g=GMm/Rm^2

g=6.67×10^-11*7.36×10^22/(1.74×10^6)^2

g=1.6ms-2

we can put the value of g=9.8ms-2

so,gm/ge=1.6/9.8=1/6

hope it helps you

Answer 2

☞︎︎︎ Solution :

$\:$

★ Let the mass of an object be m

$\:$

$\large\rightarrow \rm its \: \:weigth\: \: on \: \: moon \: \: be \: \:W _m$

$\:$

$\large\rightarrow \rm mass \: \:of \: \: moon \: \: be \: \:m_m$

$\:$

$\large\rightarrow \rm radius \: \:of \: \: moon \: \: be \: \:r_m$

$\:$

• By applying universal law of gravitation .

$\:$

$\large : \mapsto \: \boxed{\rm \: W_m = g \dfrac{m_m \times m}{ {r}^{2} _m}}$

$\:$

$\large\rightarrow \rm \: weigth \: of \: object \: on \: \: earth \\ \large \rm \: be \: \:W _e\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\:$

➪ Mass of earth = M

$\:$

➪ Radius of earth = R

$\:$

☞︎︎︎ Given :

$\:$

• Mass of earth = 5.98 × 10²⁴

$\:$

• Radius of earth = 6.37 × 10⁶

$\:$

• Mass of moon = 7.36 × 10²²

$\:$

• Radius of moon = 1.74 × 10⁶

$\:$

✞︎ Solving :

$\:$

$\large : \mapsto \: \boxed{\rm \: W_e = g \dfrac{M\times m}{ {r}^{2} }}$

$\:$

➪ Substituting the values :

$\:$

$\large :⇒ \rm W_m = g \dfrac{7.36 \times {10}^{22} \times m}{ (1.74 \times {10}^{6} m {)}^{2} }$

$\:$

$\large :⇒ \rm W_m = {2.431 \times {10}^{6} g \times m}$

$\:$

$\large :⇒ \rm W_e= {1.474 \times {10}^{11} g \times m}$

$\:$

➪ Dividing :

$\:$

$: ⇒\rm \: \dfrac{W_m}{W_e} = \dfrac{2.431 \times {10}^{10} }{1.474 \times {10}^{11} }$

$\:$

$: ⇒\rm \: \dfrac{W_m}{W_e} = 0.165 = \dfrac{1}{6}$

$\:$

∴ Weight of an object on moon = 1/6 × its Weight on earth

$\:$