Question

How to calculate the value of g? How can weight an object on the moon?

Mass of moon 7.36 X 1022 kg Radius of the moon = 1.74 X 106m

Mass of earth 5.98 X 1024kg Radius of the earth = 6.37 X 106m​

Answer 1

Answer:

Let mass of an object is ‘m’

The weight of the object on earth is We

The weight of the object on moon is Wm

Mass of the earth is M

Mass of the moon is Mm

Radius of earth is R

Radius of moon is Rm

Acceleration due to gravity on earth is ‘g’

Acceleration due to gravity on moon is ‘gm’.

Therefore,

Weight of the object on earth We = m × g

By substituting the value of ‘g’ from the expression of Universal Law of Gravitation we get

W

e

=

m

⋅

G

M

R

2

⇒

W

e

=

m

×

G

×

5.98

×

10

24

k

g

(

6.37

×

10

6

m

)

2

⇒

W

e

=

m

×

G

×

5.98

×

10

24

k

g

6.37

×

6.37

×

10

6

×

10

6

m

2

⇒

W

e

=

m

×

G

×

5.98

×

10

24

k

g

40.57

×

10

12

m

2

⇒

W

e

=

m

×

G

×

5.98

×

10

12

k

g

40.57

m

2

⇒

W

e

=

m

×

G

×

0.1474

×

10

12

k

g

m

−

2

⇒

W

e

=

m

×

G

×

1.474

×

10

11

k

g

m

−

2

Weight of the object on moon

W

m

=

m

×

g

m

By the expression of universal law of gravitation,

W

m

=

m

G

M

m

R

2

m

⇒

W

m

=

m

×

G

×

7.36

×

10

22

k

g

(

1.74

×

10

6

m

)

2

W

m

=

m

×

G

×

7.36

×

10

22

k

g

1.74

×

1.74

×

10

6

×

10

6

m

2

⇒

W

m

=

m

×

G

×

7.36

×

10

22

k

g

3.0276

×

10

12

m

2

⇒

W

m

=

m

×

G

×

7.36

×

10

10

k

g

3.0276

m

2

⇒

W

m

=

m

×

G

×

2.4309

×

10

10

k

g

m

−

2

Now,

W

m

W

e

=

m

×

G

×

2.4309

×

10

10

k

g

m

−

2

m

×

G

×

1.474

×

10

11

k

g

m

−

2

⇒

W

m

W

e

=

2.4309

1.474

×

10

⇒

W

m

W

e

=

2.4309

14.74

⇒

W

m

W

e

=

=

1

6.030

≈

1

6

Therefore, Weight of an object on moon / Weight of an object on earth = 1/6

Or, Weight of an object on the moon = 1/6th of the weight of the object on earth.

Answer 2

$\large \mathbb {\underbrace \purple{QUESTION}}$

How to calculate the value of g? How can weight an object on the moon?

Mass of moon 7.36 X 1022 kg Radius of the moon = 1.74 X 106m

Mass of earth 5.98 X 1024kg Radius of the earth = 6.37 X 106m

$\large \mathbb {\underbrace \purple{ANSWER}}$

Given that,

Mass of the Earth m1=6×1024Kg

Mass of the Moon m2=7.4×1022kg

Distance between the Earth and the Moon d=3.84×105km=3.84×108m

 Gravitational Constant G=6.7×10−11Nm2/kg2

Now, by using Newton’s law of gravitation

  F=r2Gm/1m2

 F=(3.84×108)26.7×10−11×6×1024×7.4×1022

 F=14.8225×1016297.48×1035

 F=20.069×1019

 F=20.1×1019N

Hence, the gravitational force of attraction is 20.1×10

HOPE IT WILL HELP YOU.