Question

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

Answer 1

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

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.

Answer 2

Mass of the body = 40 kg

Mass of the planet = 2 × mass of earth

Radius of the planet = 4 × radius of earth

Formula relating g, M, R :

$\boxed{\sf{g = \frac{GM}{R^{2}}}}$

For this planet, the value of g will come out to be:

$\sf{g_{0} = \frac{G(2M)}{(4R)^{2}}}$

$\sf{g_{0} = \frac{2GM}{16(R^{2})}}$

$\sf{g_{0} = \frac{GM}{8(R)^{2}}}$

$\sf{g_{0} = \frac{g}{8}}$

We have the formula of:

$\sf{W=mg}$

We put the values found:-

$\sf{W = (40)(g_{0})}$

$\sf{W=(40)(\frac{g}{8})}$

$\sf{W=5g}$

W = 5(9.8)

W = 49.0 N