# Question on gravitation and rotation of the Earth

1. Apr 30, 2015

### AakashPandita

1. The problem statement, all variables and given/known data
A body is suspended on a spring balance in a ship sailing along the equator with a speed $v'$ . If $\omega$ is the angular speed of the earth and $\omega_0$ is the scale reading when the ship is at rest , the scale reading when the ship is sailing, will be very close to
(a) $\omega_0$
(b) $(\omega_0)(1 + \frac { 2 \omega v'}{g})$
(c) $(\omega_0)(1 \mp \frac { 2 \omega v'}{g})$
(d)none of these
2. Relevant equations
Let mass of object be m
Tension in spring balance=Reading in spring balance = $\omega_0$
Tension be T when ship not sailing and Tension be T' when ship is sailing

When ship is not sailing
$mg - T = m (\omega)^2 R$
When ship is sailing
$mg - T' = m (\omega \mp v'/R)^2 R$
I solved for T' but the answer is not coming.
I could show the working but latex is hard to write.

2. Apr 30, 2015

### haruspex

But if you don't post your working nobody can tell where you are going wrong.

3. Apr 30, 2015

### AakashPandita

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4. Apr 30, 2015

### haruspex

That's fine so far, but notice that in the answers everything is expressed as a multiple of $\omega_0$. Get your answer into that form. (You will probably also need to discard some third order term.)

5. Apr 30, 2015

### AakashPandita

Wait a minute. Doesn't the value of g that we use account for the centripetal force due to rotation of earth? Is $g- (\omega)^2 R =g$ using approximation? If yes then how?

6. Apr 30, 2015

### AakashPandita

I got the answer. Thanks a lot.