A man having a mass of 50 kg begins moving on the earth and attains a speed of 1.8 m/s . What is the recoil speed of the earth? The mass of the earth is 6 × 10^ 24 kg .

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Centre of Mass, Linear momentum, Collision

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Centre of Mass, Linear momentum, Collision

A man having a mass of 50 kg begins moving on the earth and attains...

A man having a mass of

50 \text{ kg}

begins moving on the earth and attains a speed of

1.8 \text{ m/s}

. What is the recoil speed of the earth? The mass of the earth is

6 \times 10^{24} \text{ kg}

Options

A $5.4 \times 10^{-24} \text{ m/s}$
B $1.5 \times 10^{-24} \text{ m/s}$
C $1.5 \times 10^{-23} \text{ m/s}$
D $3.0 \times 10^{-23} \text{ m/s}$

Correct answer

C. $1.5 \times 10^{-23} \text{ m/s}$

Step-by-step solution

According to the law of conservation of momentum, the initial momentum of the system (Earth and man) is zero.

When the man moves, the magnitude of the momentum of the man is equal to the magnitude of the momentum of the Earth.

m v = M V

Substituting the given values:

50 \times 1.8 = 6 \times 10^{24} \times V

90 = 6 \times 10^{24} \times V

V = \dfrac{90}{6 \times 10^{24}}

V = 15 \times 10^{-24} \text{ m/s}

V = 1.5 \times 10^{-23} \text{ m/s}

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