Question

If the rotational speed of earth is increased then weight of a body at the equator

• A. increases
• B. decreases
• C. no changes
• D. increases upto a certain point and then decreases

Answer 1

The correct option is B

decreases

Explanation for correct answer:

1. Acceleration due to gravity at the equator is.

$g\text{'}=g-R_e{\omega }^2{\cos }^2\left(\lambda \right)$

$g\text{'}$= acceleration due to gravity by taking consideration of rotation of the earth, $\lambda$= latitude, $g$= acceleration due to gravity, $R_e$= earth radius, $\omega$= rotational speed

2. If $\omega$ increases, $g\text{'}$ will simultaneously decrease and the weight of the body will reduce.

3. According to Newton's law of gravity, we know $W=mg$, where $W=$Weight of the body, $m=$mass, $g=$acceleration due to gravity.

Now we can readily see that $W\propto g$, if $g$increases, $W$ increases and vice versa/

Hence Weight is directly proportional to acceleration due to gravity at any point on earth.

Thus, at the equator, if $g$decreases at equator, then $W$ will simultaneously decrease. As the mass $\left(m\right)$ is a constant quantity.

Hence the correct option is option B.

Explanation for incorrect answer:

In case of option A.

1. In the case of option A, weight cant increase as acceleration due to gravity is decreasing as rotational speed increases.
2. Hence option A is incorrect.

In case of option C

1. There must be a change in weight as acceleration is decreasing due to an increase in rotational speed.
2. Hence option C is also incorrect.

In case of option D.

1. There is no point in this explanation as acceleration will decrease only. There will not be any increase in acceleration.
2. If acceleration will decrease, then the weight will also decrease.
3. Hence option D is also incorrect.

Therefore, the correct option is option B.