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Gravitational Force

Definition: The attraction force which arises between massive bodies due to their mass is called gravitation force. → Gravitation force arises due to masses of the bodies.

Newton's Universal Law of gravity Definition: Gravitational force arises between two bodies is directly proportional to product of their masses and invesly proportional to the square of the central distance of the bodies. Gravitational force depends on Product of masses i.e.F∝ m1m2 square of the central distance i.e.F∝ $\frac{1}{\mathrm{d\; <sup>2</sup>}}$ combining above two F∝ $\frac{\mathrm{m<sub>1</sub>m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ F=G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ where, G is Gravitatonal force constant. Its value is 6.67× 10− 11 N m2/kg2 Q. Why Newton's Law of gravitation is called Universal Law ? → Because of this law is applicable every where in the universe and between every bodies having masses.

Q. In which condition F is equal to G?
→ When two bodies of masses 1/1 kg are placed 1m apart then F is equal to G.

Prove that :
Q. What is the difference between Gravitaitonal force when masses of objects are doubled. → Suppose two objects of masses m1 and m2 which are at a distance of 'd' meter.Then gravitational force F=G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ Now the masses of objects are doubled F1 = G $\frac{\mathrm{2\; m<sub>1</sub>\; 2\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ F1 = 4.G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ F1 = 4.F Hence, gravitational force is 4 times the initial force.	Q. What difference takes place between Gravitational force when masses of objects are halved. → Suppose two objects of masses m1 and m2 which are at a distance of 'd' meter.Then gravitational force F = G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ Now the masses of objects are halved F1 = G $\frac{\mathrm{(m<sub>1</sub>/2)\; (m<sub>2</sub>/2)}}{\mathrm{d\; <sup>2</sup>}}$ F1 = G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{4.d\; <sup>2</sup>}}$ F1 = $\frac{1}{4}$ F Hence, gravitational force is $\frac{1}{4}$ times the initial force.
Q. Suppose the distance between two bodies is halved then what is the difference between gravitational force from initial one. → Suppose two objects of masses m1 and m2 which are at a distance of 'd' meter.Then gravitational force F = G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ Now the distance between them is halved F1 = G $\frac{\mathrm{(m<sub>1</sub>/2)\; (m<sub>2</sub>/2)}}{\mathrm{(d/2)\; <sup>2</sup>}}$ F1 = 4.G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ F1 = 4.F Hence, gravitational force is 4 times the initial force.	Q. What happen to gravitational force when distance between two bodies is doubled. → Suppose two objects of masses m1 and m2 which are at a distance of 'd' meter.Then gravitational force F=G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{d\; <sup>2</sup>}}$ Now the the distance between two bodies is doubled F1 = G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{(2d)\; <sup>2</sup>}}$ F1 = G $\frac{\mathrm{m<sub>1</sub>\; m<sub>2</sub>}}{\mathrm{4\; d\; <sup>2</sup>}}$ F1 = $\frac{1}{4}$.F Hence, gravitational force is $\frac{1}{4}$ times the initial force.

Q. A satallite revolve around earth which doesnot require any kind of energy, why?
→ Because Satallite revolve around earth with the due to gravitational force that's why satallite doesnot require any kind of energy.
Moon doesnot require any kind of energy to revolve around earth because of force of gravity.

Effect of gravity on Earth revolve around sun Air covered around earth Water flow in the river Change in season All planets revolves around sun

Q. Gravity of earth is 6 times more than moon, what does it mean?
→ This means if a stone is 100kg on earth then this stone will be 600kg on moon.

difference between G and g
Gravitatinal constant (G)	Gravitational acceleration (g)
Gravitational force arises between body having masses 1/1kg at a distance 1m is called gravitational constant	Acceleration on falling object due to force of gravity is called gravitational acceleration.
Its remains constant every where.	Its changes inversly as radius changes
Its value = 6.67× 10-11Nm2kg-2	Its value on average = 9.8 msec-2

difference between mass (m) and weight (w) of object
mass (m)	weight
Total quantity present in object is called mass of object	Attraction force towards center applied by earth on object is called weight
Mass of the object remains same every where	Weight of the object is changes to different place
Its measurement unit is kg	Its measurement unit is N