Question

A person who weighs 150 pounds on earth would weigh 67.2 pounds on mercury. How much would a child who weighs 60 pounds on earth weigh on mercury.

Answer 1

Hint: Weight of a person or any object varies according to the gravity. While the mass of any object remains the same throughout the universe. Weight of any person is a multiple of mass and the acceleration due to gravity and we know that acceleration due to gravity “g” varies on each and every planet in the universe and hence, weight is not a constant quantity.

Complete answer:
Formula for weight (W) = mg
Where “m” is the mass of the object and “g” is the acceleration due to gravity
Let, $W_{1e}$be the weight of the person on earth and $W_{1m}$ be the weight of the person on mercury.
Let, “g” be the value of acceleration due to gravity on Earth and $g_m$ be the value of acceleration due to gravity on mercury.
Now, According to question, Weight of person on Earth = 150 pounds
Weight on Mercury = 67.2 pounds
Now, ${\displaystyle \frac{W_{1e}}{W_{1m}}}={\displaystyle \frac{mg}{m{g}_m}}$
${\displaystyle \frac{150}{67.2}}={\displaystyle \frac{mg}{m{g}_m}}$
${\displaystyle \frac{150}{67.2}}={\displaystyle \frac{g}{g_m}}$
Therefore, $g_m=0.448g$ ……………… (1)
Now, we are given that a child weight 60 pounds on mercury
 Let, $W_{2e}$be the weight of the child on earth and $W_{2m}$ be the weight of the child on mercury
${\displaystyle \frac{W_{2e}}{W_{2m}}}={\displaystyle \frac{mg}{m{g}_m}}$
Putting the values of weight and $g_m$, we get
$${\displaystyle \frac{60}{W_{2m}}}={\displaystyle \frac{g}{0.448g}}$$
$W_{2m}=26.88Pounds$
Therefore, the weight of a child on mars is 26.88 Pounds.

Note:
Gravitational pull on mercury is almost half as that of earth, and hence a person’s weight will be less on mercury than on earth. While if we talk about Giant planets that have very strong gravitational pull then, the weight of the object or person will be less on earth as compared to giant planets like Jupiter, Saturn etc.