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JIPMER 2008

Exam: JIPMER
Year: 2008
Subject: Physics
Chapter: Gravitation

JIPMER 2008 · Physics · Gravitation

The speed of earth's rotation about its axis is ω . Its speed is...

The speed of earth's rotation about its axis is

\omega

. Its speed is increased to

x

times to make the effective acceleration due to gravity equal to zero at the equator. Then

x

is

Options

A $1$
B $8.5$
C $17$
D $34$

Correct answer

C. $17$

Step-by-step solution

Earth rotates about its own axis in 24 h . So,

\quad T=24 \times 60 \times 60 \mathrm{~s}

So, angular speed of earth about its own axis

\omega=\frac{2 \pi}{T}=\frac{2 \pi}{24 \times 60 \times 60} \mathrm{rad} / \mathrm{s}

At equator,

g^{\prime}=g-R_e \omega^{\prime 2}

or

\quad 0=g-R_e \omega^{\prime 2}

or

\omega^{\prime}=\sqrt{\frac{g}{R_e}}=\frac{2 \pi}{84.6 \times 60}

\therefore \quad \frac{\omega^{\prime}}{\omega}=\frac{24 \times 60 \times 60}{84.6 \times 60} \approx 17

\Rightarrow \quad \omega^{\prime}=17 \omega

So, value of

x

is 17 .

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