Class 10 Science I Gravitation

The mass and weight of an object on earth are 5 kg and 49 N respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is 1/6th of that on the earth.

As per the given data, we can list the data as,

mass on earth , m = 5kg

Weight on earth, W= 49N

$g_{m}=\frac{g_{e}}{6}$

To fnd , mass on moon m' = ?

weight on moon W' = ?

Solution -

As we know that mass of an object remain remains constant irrespective of the place,

hence , mass on earth = mass on moon

m' = 5kg

We know that weight W = m x g

writing this equation for earth and moon ,

For earth,

$W=m\textrm{x}g_{e}$

For moon
$W^{'}=m\textrm{x}g_{m}$

taking the ratio of the above two equation, we have

$\frac{W^{'}}{W}=\frac{mg_{m}}{mg_{e}}=\frac{g_{m}}{g_{e}}$

$\frac{W^{'}}{W}=\frac{1}{6}$

$W^{'}=\frac{W}{6}=\frac{49}{6}=8.166N=8.17N$

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?