Question

2. Let us consider the force of gravitation between two objects as F and distance between
them as r What will be the effect on force if
(a) r is reduced to ¼ th and
b) masses of both the objects are increased by 3 times?​

Answer 1

Answer:

Ans. The force of gravitation between two objects is inversely proportional to the square of the distance between them therefore the gravity will become four times if distance between them is reduced to half.

plzzz follow

Answer 2

(a) Gravitational force will become 16 times the force F ⇒ F' = 16 F

(b) Gravitational force will become 9 times the force F ⇒ F' = 9 F

Step-by-step Explanation:

Given: Gravitational Force = F

Distance between the two objects = r

To Find: The effect on the force when (a) r is reduced to ¼ th and (b) masses of both the objects are increased by 3 times

Solution:

• The formula for gravitational force

Consider a gravitational force F acting between the two objects having masses m₁ and m₂ respectively separated by the distance r. Therefore, the gravitational force is;

$F = {G m_1 m_2}\\{} \ \ \ \ \ \ \overline{ \ \ \ \ r^{2} \ \ \ \ }$

• The effect on the force when r is reduced to ¼ th

When 'r' is reduced to ¼ th ⇒ r' = r/4,  we get,

$F' = {G m_1 m_2}\\{} \ \ \ \ \ \ \overline{ \ \ \ \ {(\frac{r}{4}})^{2} \ \ \ \ }$

⇒ $F' = 16 {G m_1 m_2}\\{} \ \ \ \ \ \ \ \overline{\ \ \ \ \ \ \ r^{2} \ \ \ \ }$

⇒ F' = 16F

• The effect on the force when masses of both the objects are increased by 3 times

When the masses m₁ and m₂ are increased by 3 times ⇒ m₁' = 3m₁ and m₂' = 3m₂, we get,

$F' = {G (3m_1)(3 m_2)}\\{} \ \ \ \ \ \ \ \overline{ \ \ \ \ \ \ \ \ {r}^{2} \ \ \ \ \ \ \ \ }$

⇒ $F' = 9 {G m_1 m_2}\\{} \ \ \ \ \ \ \ \overline{\ \ \ \ \ \ \ r^{2} \ \ \ \ }$

⇒ F' = 9F

Hence, the gravitational force (F') will become 16 times the force F when r is reduced to ¼ th, while it will become 9 times the force F when the masses are increased by 3 times.