Question

If the radius of the Earth contracts by $1\%$ and mass remains the same, what would be the effect on our weight?

• A. Increases
• B. Decreases
• C. Remains the same
• D. Becomes zero

Answer 1

The correct option is A Increases

On the Earth, acceleration due to gravity is given by:
$g=\frac{GM}{R^2}$​
where:
${}^{\prime }{G}^{\prime }$ is the gravitational constant
${}^{\prime }{M}^{\prime }$ is the mass of the Earth
${}^{\prime }{R}^{\prime }$ is the radius of the Earth.

As the value of ${}^{\prime }{R}^{\prime }$ decreases, the value of 'g' would increase. Weight is given by mg and so the weight also increases. In fact, the weight increases by approximately $2\%$.