Question

the mass of body is 40 kilogram find the weight of body on the surface of a Planet whose mass is doubled then the mass of the earth and radius is 4 times the radius of the earth​

Answer 1

Answer:

W = 49 N

Explanation:

Let M & M' be mass of earth & given planet. Also R & R' be their radius respectively.

Given is -

M' = 2M

R' = 4R

Gravitational accelaration on earth surface is -

g = GM / R^2

Gravitational accelaration on supposed planet is -

g' = G(2M) / (4R)^2

g' = GM / 8R^2

g' = g / 8

g' = 9.8 / 8

g' = 1.225 m/s^2

Weight of the body on planet is -

W = mg'

W = 40 × 1.225

W = 49 N

Therefore weight of body on planet is 49 N

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Answer 2

$\bold{\underline{\underline{Answer:}}}$

Weight of the body = 49 N

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :

• The mass of body is 40 kilogram
• Mass of a planet is doubled the mass of the earth
• Radius of the planet is 4 times the radius of the earth.

To find :

• Weight of the body on the surface of the planet.

Solution :

For Earth :

Let M be the mass.

Let R be the radius.

G be the universal constant of gravitation.

Let g be the gravitational acceleration.

•°• g = $\bold{\frac{GM}{R^2}}$ ---> (1)

For Planet :

Mass = 2M

Radius = 4R

g' = Gravitational acceleration

•°• g' = $\bold{\frac{G2M}{(4R) ^2}}$

g'= $\bold{\frac{G2M}{4R\times\:4R}}$

g' = $\bold{\frac{GM}{2R\:\times4R}}$

g' = $\bold{\frac{GM}{8R^2}}$ ---> (2)

From equation 1, g = $\bold{\frac{GM}{R^2}}$

g' = $\bold{\frac{g}{8}}$

g' = $\bold{\frac{9.8}{8}}$

g' = 1.225 m/s²

Now to calculate the weight of the body of mass 40 kg on planet, we will use the formula :-

$\bold{\large{\red{\rm{W\:=\:mg}}}}$

But since we are calculating the weight on the Planet, we will consider the value of g' instead of g.

•°• Formula :-

$\bold{\large{\red{\rm{W\:=\:mg'}}}}$

Now simply block in the values,

$\bold{W\:=\:40\times\:1.225}$

$\bold{W\:=\:49N}$

•°• Weight of the body on Planet will be 49 N.