Question

An object weighs 294N on the earth.
a) What would be its mass on the moon?
b) What is the acceleration due to gravity on the moon?

Answer 1

Explanation:

Objects weight on earth = 250 N

The objects mass = (250 / 9.81) = 25.49 Kg.

The objects weight on the moon = 25.49 * 1.625 = 41.41 N.

[Note-1: The acceleration due to gravity on the surface of the Moon is about 1.625 m/s2]

[Note-2: weight = mass x gravity]

Answer 2

The mass of the object on moon will be 30kg and the acceleration due to gravity on the moon is 1/6th of that of the earth.

a) Calculating the mass of the object on the moon:

The mass of the object on the earth and the moon remains the same as it is not dependent on the acceleration due to gravity.

Weight of the object on earth= $W_{e}$= $294 Newton$

Let us suppose the mass of the object on moon = $m_{e}$

Acceleration due to gravity on earth = $g_{e}$ = $9.8 m/s^{2}$

We already know that   $W_{e}$ = $m_{e}$ ×$g_{e}$

Substituting the values

$294 = m_{e}$ ×$9.8$

$m_{e}$ = $\frac{294}{9.8}$

$m_{e}$ = $30 kg$

Since, the mass on the earth and the moon remains the same, hence, the mass of the object on the moon is 30 kg.

b) The acceleration due to gravity formula is given by

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

Here,

G is called as universal gravitational constant:

the value of G = $6.674$×$10^{-11}m^{3} kg^{-1} s^{-2}$

M is called as the mass of the massive body.

R is called as the radius of the massive body.

g is called as the acceleration due to gravity.

mass of the moon = $7.35$ ×$10^{22} kg$

radius of the moon = $1.74$ ×$10^{6}$ $m$

Substituting the values in the formula $g = \frac{GM}{R^{2} }$

Hence, the value of g on moon is $g=1.625 m/s^{2}$

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