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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Rotational Mechanics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rotational Mechanics

Due to friction between ocean water and the earth's surface, the...

Due to friction between ocean water and the earth's surface, the rotational kinetic energy of the earth continuously decreases. Determine the average torque of friction on the earth if its angular speed decreases by

0.0016 \text{ rad/day}

over a period of

100

years. The mass of the earth is

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

and its radius is

6400 \text{ km}

.

Options

A $5.8 \times 10^{20} \text{ N m}$
B $1.5 \times 10^{21} \text{ N m}$
C $2.9 \times 10^{20} \text{ N m}$
D $5.8 \times 10^{22} \text{ N m}$

Correct answer

A. $5.8 \times 10^{20} \text{ N m}$

Step-by-step solution

The average torque of friction is

5.8 \times 10^{20} \text{ N m}

.

Initial parameters for the moment of inertia

I = \dfrac{2}{5}MR^2

and angular kinematics are validated.

Standard processing applied for unit conversions to SI units.

\tau = I \dfrac{\Delta \omega}{\Delta t} = (9.83 \times 10^{37}) \times \dfrac{1.85 \times 10^{-8}}{3.15 \times 10^9}

\tau \approx 5.8 \times 10^{20} \text{ N m}

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