Question

If the radius of the earth is made three times, keeping the mass constant, then the weight of a body on the earth's surface will be as compared to its previous value is

• A. one third
• B. one ninth
• C. three times
• D. nine times

Answer 1

The correct option is B one ninth

Weight is nothing but mass multiplied by the acceleration due to gravity

ie $W=mg$ ............(1)

If Mass of earth is $M$ and radius is $r$ then gravitational acceleration, $g=GM/r^2$

According to question, radius is increased by three times

ie $r^{\prime }=3r$

$g^{\prime }=GM/(3r{)}^2=GM/9r^2=\frac{g}{9}$

$g^{\prime }=\frac{g}{9}$

As gravity became one-ninth so from equation (1) the weight will also become one-ninth because mass of the body remain same.