GRAVITATION

6 )

Correct form of gravitational law is

Select correct option from the following options

(A) F = – [(Gm₁m₂) / r²]

(B) F^➙ = – [(Gm₁m₂) / r²]

(B) F^➙ = – [(Gm₁m₂) / r³] r^➙

View Solution

Answer :

7 )

Mass M is divided into two parts xM and (1 – x) M. For a given separation, the value of x for which the gravitational force between the two pieces becomes maximum is

1/2

4/5

View Solution

Answer :

F = [(Gm₁m₂) / r²]

i.e. F ∝ m₁m₂

F ∝ mx(1 – x)m

F ∝ m² ∙ x(1 – x)

for maximum force

(dF / dx) = 0

(d/dx) = [x(1 – x)m²] = 0

m²[– 2x + 1] = 0

x = (1/2)

8 )

The earth (mass = 6 × 10²⁴ kg) revolves around the sun with angular velocity 2 × 10^–7 rad/sec in a circular orbit of radius 1.5 × 10⁸ km. The force exerted by the sun on the earth is = ………… N

Select correct option from following options

(A) 18 × 10²⁵ (B) zero

View Solution

Answer :

Force exerted by sun of earth = mw²R

given = m = 6 × 10²⁴ kg.

w = 2 × 10^–7 rad/s

R = 1.5 × 10⁸ km

∴ F = (6 × 10²⁴)(2 × 10^–7)² (1.5 × 10⁸ × 10³)

= 36 × 10²¹ N

9 )

Two particle of equal mass go round a circle of radius r. Under the action of their mutual gravitational force. The speed of each particle is = …………..

Æ² = (1 / 2r) âˆš(1 / Gm)

Æ² = âˆš(Gm / 2r)

Æ² = (1/2)âˆš(Gm / r)

Æ² = âˆš[(4Gm) / r]

View Solution

Answer :

Centripetal force = gravitational force

(mv² / r) = [{G ∙ (m)(m)} / {(2r)²}]------here m₁ = m₂ = m

V² = (Gm / 4r)

V = (1/2)√(Gm / r)

10 )

The distance of the moon and earth is D the mass of earth is 81 times the mass of moon. At what distance from the center of the earth, the gravitational force will be zero

D/2

[(12D) / 3]

(4D / 3)

(9D / 10)

View Solution

Answer :

Let that point be P where F = 0 given m₁ = 81 m₂

F_PA = F_PB

[(G ∙ m₁m₂) / x²] = [(Gm₂∙ m) / (D – x²)]

(m₁ / x²) = [m₂ / (D – x)²]

(m₁/m₂) = [x² / (D – x)²]

√(m₁ / m₂) = [x / (D – x)]

D√(m₁) – x√(m₁) = √(m₂) ∙ x

D ∙ √(m₁) = x[√(m₂) + √(m₁)]

x = [{D√(m₁)} / {√(m₁) + √(m₂)}]

m₁ = 81 m₂

hence

x = [{D ∙ √(81 m₂)} / {√(81 m₂) + √(m₂)}]

= (9D / 10)

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