Chapter 4, Problem 53A

a.

To determine

Weight of a given mass on the surface of Mercury.

Answer to Problem 53A

Weight on the surface of Mercury is 22.34 N.

Explanation of Solution

Given :

Mass is $m=6\text{ kg}$

Acceleration due to gravity on mercury is 0.38 times of gravity on earth.

Formula used:

The weight of the body is,

  $W=mg$

Where,

m is mass

g is acceleration due to gravity.

Calculation:

Acceleration due to gravity on earth is $g=9.8{\text{ m/s}}^2$

It is given acceleration due to gravity on mercury is 0.38 times of gravity on earth.

Therefore, acceleration due to gravity on mercury is,

  $\begin{array}{l}{g}_m=0.38\times 9.8\\ =3.724{\text{ m/s}}^2\end{array}$

Weight on the surface of Mercury is,

  $\begin{array}{c}W=m{g}_m\\ =6\times 3.724\\ =22.34\text{ N}\end{array}$

Conclusion:

Therefore, weight on mercury is 22.34 N

b.

To determine

Weight of a given mass on the surface of Pluto.

Answer to Problem 53A

Weight on the surface of Pluto is 2.09 N

Explanation of Solution

Given :

Mass is given $m=7\text{ kg}$

Acceleration due to gravity on Pluto is 0.08 times of gravity on Mercury.

Formula used :

The weight of the body is.

  $W=mg$

Where, m is mass and g is acceleration due to gravity.

Calculation:

From previous subpart, acceleration due to gravity on Mercury is $g_m=3.724{\text{ m/s}}^2$

Now,

It is given acceleration due to gravity on Pluto is 0.08 times of gravity on Mercury.

Therefore, acceleration due to gravity on Pluto is;

  $\begin{array}{c}{g}_p=0.08\times 3.724\\ =0.29792{\text{ m/s}}^2\end{array}$

Weight is given by,

  $W=m{g}_p$

Here, m is mass and $g_p$ is acceleration due to gravity on Pluto .

  $\begin{array}{c}W=m{g}_p\\ =7\times 0.29792\\ =2.085\text{N}\\ \approx 2.09\text{ N}\end{array}$

Conclusion:

Therefore, weight on Pluto is 2.09 N