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.

R be the radius. G be the universal constant of gravitation.

Let g be the gravitational acceleration.

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

For Planet :

Mass = 2M

Mass = 2MRadius = 4R

g' = Gravitational acceleration

•°• g' = $\bold{\dfrac{G2M}{(4R) ^2}}$

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

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

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

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

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

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

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

Answer:

Weight of body on planet is 49N