GRAVITATION

1 )

Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational force between them is proportional to

Select correct option from the following options

(A) R² (B) R^–2 (C) R^–4 (D) R⁴

View Solution

Answer :

Gravitational force = F = [(G ∙ m₁ ∙ m₂) / D²]

where m₁, m₂ are masses of two bodies

D is distance between them.

Given : sphere are identical

hence F = [{G(m)(m)} / (2R)²]

= [{G(ρ ∙ V)²} / (4R²)]------------ as mass = density × volume

i.e. m = ρv

= [(Gρ²) / (4R²)][(4/3)πR³]² ---------- sphere volume = (4/3)πR³

F = (4/3)π²ρ²R⁴

F ∝ R⁴

2 )

The gravitational force Fg between two objects does not depend on

Sum of the masses

Product of masses

Gravitational constant

Distance between the masses

View Solution

Answer :

F_{Gravitational} = F = [(G ∙ m₁ ∙ m₂) / D₂]

m₁, m₂ are masses of bodies and D is distance between them.

G = Gravitational constant.

hence option A is the answer

3 )

The atmosphere is held to the earth by

Clouds

Gravity

Winds

None of the above

View Solution

Answer :

Atmosphere is held to earth by gravity.

4 )

Two sphere of mass m₁ and m₂ are situated in air and the gravitational force between them is F. The space around the masses is now filled with liquid of specific gravity 3. The gravitational force will now be

F/3

F/9

View Solution

Answer :

Gravitational force does not depend on medium. Hence force F remains unchanged

5 )

A satellite of the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly disappears, the satellite will

Continue to move with velocity v along the original orbit.

Move with a Velocity v, tangentially to the original orbit.

Fall down with increasing velocity.

Ultimately come to rest somewhere on the original orbit.

View Solution

Answer :

in circular path with necessary centripetal force is removed then body moves in tangential path. Hence if gravitational force is removed satellite will move tangentially to original orbit.

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