Question

(
12. If a body's weight is 36 kg on the surface of the earth, how much would it
weight on the surface of a planet whose mass is 1/9 and radius 1/3 of the earth
(a) 32 kg
(b) 36 kg
(c) 12 kg
(d) 10 kg​

Answer 1

Answer:

b

Explanation:

Answer

g=  

r  

2

 

Gm

​  

 

g=  

(  

3

r

​  

)  

2

 

G  

9

m

​  

 

​  

x  

r  

2

 

Gm/9

​  

=  

r  

2

 

Gm

​  

 

∴ same weight  

36kg

Answer 2

Given data :

A body's weight is 36 kg on the surface of the earth.

Mass of other planet is 1/9 and radius 1/3 of the earth.

Solution : Now, here ;

⟹ M = Mass of the Earth

⟹ R = Radius of the Earth

Now, according given,

Mass of the planet = M/9

Radius of the planet = R/3

We know ;

⟹ g = acceleration due to gravity on the earth's surface

Where,

⟹ g = 9.8 m/s²

Now, acceleration due to gravity

⟹ g = GM/R² = 9.8 m/s² ----{ 1 }

Now, to find acceleration due to gravity on surface of the planet.

Let, acceleration due to gravity on the surface of the planet be g'

⟹ g' = [G * (M/9)]/(R/3)²

⟹ g' = [G * (M/9)]/(R²/9)

{9 cancelled}

⟹ g' = GM/R² ----{ 2 }

From eq. { 1 } and eq. { 2 }

⟹ g' = g ----{ 3 }

Hence, we know that acceleration due to gravity on surface of the planet is equal to the acceleration due to gravity on the earth's surface.

∴ g' = 9.8 m/s²

Here we know;

Mass does not change whether it is measured on Earth or other planet. Hence weight is measured by formula ;

⟹ weight = mass * acceleration due to gravity

Now, from eq. { 3 } and given we know that weight of body is same on the both planet. (where one planet is earth)

Answer : Hence, weight of the body on the surface of the planet is 36 kg. {( b ) 36 kg}.