Gravitational (numericals) for SEE

TYPE 1

Theory

Newton’s law of gravitation states that. The mutual force of attraction between any two bodies is directly proportional to the product of their mass and inversely proportional to the square of the distance between their centres.`

Let the masses of two bodies be M₁ and M₂ , the distance between their centres be d or r and mutual force of attraction be F.

Then, according to Newton`s law of gravitation,

F∝ M₁M₂……………………….eqn (1)

F∝1/d²………………………………eqn (2)

On combining equation 1 and 2, we get ,

$F=G\frac{m_1{m}_2}{r^2}$

here G is gravitational constant whose value is 6.67*10^-11 Nm²/kg² .

solved numerical 1

what is the mutual force of attraction berween the sun and the jupiter if their masses are 2*10³⁰ kg and 1.9*10²⁷ kg and are at a distance of 78*10⁷ km?

solution =

mass of sun ( M₁ )= 2*10³⁰ kg

mass of jupiter( M₂)=1.9*10²⁷ kg

distance between their centres(r)= of 78*10⁷ km= 78*10¹⁰ m note 1km=1000m

gravitational force (F)=?

we know that , the value of Gravitational constant is 6.67*10^-11 Nm²/kg² .

we have ,

$F=G\frac{m_1{m}_2}{r^2}$ [ this formula is used to calculate the gravitational force between any two bodies]

=6.67*10^-11 *2*10³⁰ *1.9*10²⁷ /[ 78*10¹⁰ ]² { putting all the values of above quantities }

=6.67*2*1.9*10^-11+30+27 /[ 78*10¹⁰ ]² {here all the power of the numerator is added}

=4.166*10²³ N

The gravitational force between the sun and Jupiter is 4.166*10²³ N.

Similar questions for practice

1. What is the gravitational force between the Earth and Mars? If the mass of the Earth is 5.97×10²⁴ kg, the mass of Mars is 6.42*10²⁴ kg and distance between the Earth and Mars is 2.25*10⁸ m.
2. Calculate the gravitational force between the Earth and Moon. If the masses of the Earth and Moon are 5.97×10^24 kg and 7.2×10^23 kg, respectively, and the distance between them is 384,400 km.