Question

The mass of moon is 7.2 x 10^22 kg and its radius is 1.7 *10^6 m Calculate the acceleration due to gravity of moon and also the weight of a person having mass 80 kg?​

Answer 1

Answer:

Acceleration due to gravity, g= GM/ r^2

G = Gravitational constant = 6.674 × 10^-11 m^3 / kg-s

M= mass of moon

r= radius of moon

g= 6.674× 10 ^-11 × 7.2× 10^22 / ( 1.7 × 10^6)^2

g = 1.6 m/s^2

Weight of the person

w= mg

w = 80 × 1.6

w = 128kg

Answer 2

$\underline{\underline{\sf SOLUTION : }}$

Here we are provided mass of moon as 7.2 × 10²² kg and its radius is 1.7 × 10⁶ m and we are asked to find the acceleration due to gravity of moon and weight of person having mass 80 kg.

So, to solve this question first we have to find the acceleration due gravity of moon by using given below formula :

$\bullet\:\sf g_{(moon)} = \dfrac{GM_{(moon)}}{ \bigg(R_{(moon)} \bigg)^{2} }$

Here,

$\dag \sf\:g_{(moon)} = Acceleration \: due \: to \: gravity \: of \: moon$

$\dag \sf\: G= Gravitational \: constant$

$\dag \sf\:M_{(moon)} = Mass \: of \: moon$

$\dag \sf\:R_{(moon)} = Radius \: of \: moon$

The value of Gravitational constant (G) is 6.673 × 10⁻¹¹ Nm²kg⁻²

$\bigstar \: \underline{\underline{\textsf{ According to the Question Now :}}}$

$:\implies \sf g_{(moon)} = \dfrac{GM_{(moon)}}{\bigg(R_{(moon)}\bigg)^2}$

$:\implies \sf g_{(moon)} = \dfrac{6.673 \times {10}^{ - 11} \times 7.2 × {10}^{22} }{(1.7 \times {10}^{6})^{2} }$

$:\implies \sf g_{(moon)} = \dfrac{48.0456 \times {10}^{11} }{2.89 \times {10}^{12} }$

$:\implies \sf g_{(moon)} = \dfrac{48.0456 \times {10}^{11}\times {10}^{ - 12} }{2.89 }$

$:\implies \sf g_{(moon)} = \dfrac{48.0456 \times {10}^{ - 1} }{2.89 }$

$:\implies \sf g_{(moon)} =16.62\times {10}^{ - 1}$

$:\implies\underline{\boxed{ \sf g_{(moon)} =1.662 \:m/s^2}}$

Now, we have find the acceleration due to gravity of moon but we are also asked to find the weight of person having mass 80 kg. So, Let's do it :

$\dashrightarrow\:\:\sf Weight_{(of person) }= Mass \times Acceleration \: due \: to \: gravity_{(of \: moon)}$

$\dashrightarrow\:\:\sf Weight_{(of person) }=80 \times 1.662$

$\dashrightarrow\:\:\underline{\boxed{\sf Weight_{(of person) }=132.96\:N}}$