Question

A heavenly body has mass one third of the earth and its radius is half as that of the earth. if stone weights 200 newton on the earth's surface,find its weight on that heavenly body

Answer 1

Let mass of earth = M
∴mass of heavenly body = M/3
Let radius of earth = R
∴ radius of heavenly body = R/2

From Gravitational law,
g = GM/R² , here g is acceleration due to gravity on Earth's surface.

But for heavenly surface
g' = GM/3/(R/2)² = 4GM/3R²
= (4/3) GM/R² = (4/3)g

Hence, acceleration due to gravity on heavenly's surface is 4/3 times of acceleration due to gravity on earth surface.

Given, weight of body on Earth's surface = 200 N
∴ weight of body on heavenly's surface = 200 × 4/3 = 800/3 = 266.67 N

Hence, answer is 266.67 N

Answer 2

Hello Dear.

Here is the answer---


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Let the Acceleration due to gravity on the earth be g and on the Heavenly Body be g'.

Let the Mass and the Radius of the Earth be m and r.

According to the Question,
  
   Mass of the Heavenly Body = (1/3) Mass of the Earth
                                                = m/3

  Radius of the Heavenly Body = (1/2) Radius of the Earth
                                                 = r/2


Now,

  Using the Relation between the g( Acceleration due to Gravity) and G (Gravitational Constant),

                           g = Gm/r²  -------------------eq(i)

For the Heavenly Body,

                     g' = (G × m/3)/(r/2)²
                ⇒ g' =  4 × G m/3r²
               ⇒ g' = (4/3) Gm/r²
         
   Using eq(i),

              g' = (4/3) × g  ----------------------eq(ii)

Thus, acceleration due to gravity on the Heavenly Body is (4/3)rd of the Earth.


As per as the Question,

On the Earth,
 
     Weights of the Stone = 200 N.

Using the Formula,
           
             W = Mass × g
            Mass = W/g

On the Heavenly Body,

   Let the Weights of the stone be W'

Thus, W' = Mass × g'
        Mass = W'/g'

We know, the mass of the object does not changes from place to place.It always remains same.

Thus,       
     Mass of Stone on Earth = Mass of Stone on Heavenly Body
                                    W/g = W'/g'

               Using eq(ii),
                       
                        $\frac{200}{g} = \frac{W'}{4g/3}$
                            W' = 200 × (4/3)
                            W' = 266.67 N.

Thus, the weights of the object on the Heavenly body is 266.67 N.


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Hope it helps.


Have a Marvelous Day.