Question

a) A person weighs 110.84N on moon, whose acceleration due to gravity is 1/6

of the earth. If the value of ‘g’ on earth is 9.8m/s2

. Calculate.

i) ‘g’ on moon

ii) mass of person on moon

iii) weight of person on earth

b) How does the value of g on the earth is related to the mass of the earth and

its radius?​

Answer 1

Question (a):-

Given:-

• Weight of person on the Moon is 110.84 N.

• Acceleration due to gravity of the moon is 1/6 of the earth.

• Value of ' g ' on the earth is 9.8 m/s².

To Find:-

• ' g ' on the moon.

• mass of person on moon.

• weight of person on the earth.

Solution:-

(1)   Here, We know that acceleration due to gravity of the moon is 1/6 of the earth.

And, Acceleration due to gravity of the earth is " 9.8 m/s² ".

So, $\dfrac{" g " on \ the \ earth}{6}$

⇒  $\dfrac{9.8}{6}$

⇒  1.63 m/s²    

Hence, Acceleration due to gravity on the moon is 1.63 m/s².

(2)  Relation between mass and weight:-

Weight = Mass × Acceleration due to gravity of that body

So, putting the respective value we get,

110.84 N = Mass × 1.63 m/s²

Mass = $\dfrac{110.84}{1.63}$

Mass = 68 kg

Hence, Mass of the body on the moon is 68 kg.

(3) From above relation between mass and weight:-

We get,

Weight = 68 kg × 9.8 m/s²     [ Since mass is constant of any body on any planet ]

Weight = 666.4 N

Hence, Weight of the body on the earth is 666.4 N.

Question (b) Solution:-

Here, Let we drop a body of mass m from a distance of R from the center of the Earth of mass M, then the force exerted by the earth on the body is given by law of gravitation as :-

$F = G \times \dfrac{M \times m}{R^{2}}$                --------------------- (1)

Now, The force exerted to produce acceleration in the body due to which the body moves downwards is given by :-

$F = m \times a$

So, Acceleration of the body = $a = \dfrac{F}{m}$            --------------- (2)

Now, Putting the value of force F from equation (1) in the above relation, We get:-

        Acceleration,  $a = \dfrac{G \times M \times m}{R^{2} \times m}$

         or                    $a = G \times \dfrac{M}{R^{2}}$

Since, The acceleration produced by the earth is known as acceleration due to gravity and represented by the symbol g. So, by writing 'g' in place of 'a' in the above equation, we get :

Acceleration due to gravity,  $g = G \times \dfrac{M}{R^{2}}$

                            Where, G = gravitational constant

                                         M = mass of the earth

                                          R = Radius of the earth

Hence, That's how the value of g on the earth is related to the mass of the earth and it's radius.