The mass and weight of an object on earth are $ 5 \mathrm{~kg} $ and $ 49 \mathrm{~N} $ respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is $ 1 / 6 $ th of that on the earth.
Given,
Mass of an object on Earth = 5 kg
Weight of an object on Earth = 49 N
${g}_{m}=\frac{1}{6}{g}_{e}$ $({g}_{m}\ is\ the\ gravity\ of \ moon,\ and\ {g}_{e}=accelration\ due\ to\ gravity\ on\ earth)$
To find: Values of mass and weight on Moon.
Solution:
We know that,
$W=mg$
where, W is Weight, m is mass, g is the acceleration due to gravity
${W}_{e}=m{g}_{e}$
$49=5\times {g}_{e}$
${g}_{e}=9.8m/{s}^{2}$
Hence, gravity on the earth is 9.8 m/s2
According to the relation given,
${g}_{m}=\frac{1}{6}{g}_{e}=\frac{1}{6}\times {9.8}$
${g}_{m}=1.633m/s^2$
Hence, gravity on the moon is 1.633 m/s2
$\therefore Weight\ on\ moon=m{g}_{m}$
$=5\times {1.633}$
$=8.166N$
The value of weight will be 8.166 N on the Moon.
On the other hand, the value of mass will be the same as the earth (i.e 5kg) on the moon as it is a constant quantity.
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