Question

If planet existed whose mass and radius were both half of the earth, the acceleration due to gravity at the surface would be:

• A. $19.6m{s}^{-2}$
• B. $9.8m{s}^{-2}$
• C. $4.9m{s}^{-2}$
• D. $2.45m{s}^{-2}$

Answer 1

The correct option is A

$19.6m{s}^{-2}$

Explanation

Step 1: Acceleration due to gravity

$g=\frac{GM}{R^2}$

$M=$mass of the planet

$R=$radius on earth

G = Universal gravitational constant

Step 2: Calculating Acceleration due to gravity on this planet

Let's assume that g' is the acceleration due to gravity on this planet

$g\text{'}=\frac{G\left({\displaystyle \frac{M}{2}}\right)}{{\left({\displaystyle \frac{R}{2}}\right)}^2}$ $\left(asM=\frac{M}{2}R=\frac{R}{2}botharehalfed\right)$

$g\text{'}=\frac{2GM}{R}$

$g\text{'}=2g\left(asg=\frac{GM}{R}thevalueofg=9.8\right)$

$=2\times 9.8=19.6m/s^2$

Thus, acceleration due to gravity at the surface is $g\text{'}=19.6m/s^2$.

Hence option ‘a’ is correct.