The gravitational force exerted on a 1 g particle by a similar particle is 6.67 × 10^ -17 N . Determine the separation between the particles.

Correct answer: C. 1 m Given mass of each particle, m_1 = m_2 = 1 g = 10^ -3 kg Gravitational force between the particles, F = 6.67 × 10^ -17 N Universal gravitational constant, G = 6.67 × 10^ -11 N m^2kg^ -2 The gravitational force is given by Newton's law of gravitation: F = (G m_1 m_2)/(r^2) Substituting the given values: 6.67 × 10^ -17 = 6.67 × 10^ -11 × 10^ -3 × 10^ -3 r^2 6.67 × 10^ -17 = 6.67 × 10^ -17 r^2 r^2 = 1 r = 1 m

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: The Forces

Concepts Of Physics MCQ Edition [Volume 1] · Physics · The Forces

The gravitational force exerted on a 1 g particle by a similar...

The gravitational force exerted on a

1 \text{ g}

particle by a similar particle is

6.67 \times 10^{-17} \text{ N}

. Determine the separation between the particles.

Options

A $10 \text{ m}$
B $1000 \text{ m}$
C $1 \text{ m}$
D $0.1 \text{ m}$

Correct answer

C. $1 \text{ m}$

Step-by-step solution

Given mass of each particle,

m_1 = m_2 = 1 \text{ g} = 10^{-3} \text{ kg}

Gravitational force between the particles,

F = 6.67 \times 10^{-17} \text{ N}

Universal gravitational constant,

G = 6.67 \times 10^{-11} \text{ N m}^2\text{kg}^{-2}

The gravitational force is given by Newton's law of gravitation:

F = \dfrac{G m_1 m_2}{r^2}

Substituting the given values:

6.67 \times 10^{-17} = \dfrac{6.67 \times 10^{-11} \times 10^{-3} \times 10^{-3}}{r^2}

6.67 \times 10^{-17} = \dfrac{6.67 \times 10^{-17}}{r^2}

r^2 = 1

r = 1 \text{ m}

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