Question

A person weigh 110.84N on the moon, whose acceleration due to gravity is 1/6 of that earth. If the value of g on the earth is 9.8 m/s2. calculate, (1) "g" on the earth (2) Mass of person on moon (3) Weight of person on the earth

Answer 1

Given :

weight of person in moon - 110.84N

acceleration due to gravity is 1/6 of that earth

acceleration due to gravity = 9.8 m/s²

To Find :

(1) "g" on the moon

(2) Mass of person on moon

(3) Weight of person on the earth

Solution :

(1) It is given that the value of acceleration due to gravity (g) of moon is $\frac{1}{6}$ that of earth.

       'g' on earth = 9.8 m/s²

Acceleration due to gravity on moon = $\frac{g}{6}$

                                                              = $\frac{9.8}{6}$

                                                              = 1.63 m/sec²

(2) We know,

          Weight (w) = mass on moon(m) × acceleration due to gravity (g)

or,       mass of person on moon (m) = $\frac{w}{g}$

                                                            = $\frac{110.84}{1.63}$

                                                            = 68 Kg

(3) Weight of person on earth = mass × acceleration due to gravity on earth

    Weight of person on earth = 68 × 9.8

(as mass can neither be created nor be destroyed, so mass of person in the moon = mass of person in earth)

                                                 = 666.4 N

               

   

Answer 2

Given:

Weight of person on moon = 110.84 N

Acceleration due to gravity of moon = $\frac{1}{6} *$ acceleration due to gravity of earth

gravitational acceleration on earth = 9.8 m/$s^{2}$

To Find: (1) 'g' on moon, (2) Mass of person on moon, (3) Weight of person on earth.

Calculation:

• Weight of an object is expressed as multiplication of mass of the object and gravitational acceleration of the planet.
• Weight of body is defined as the force of gravity exerted on the body by the ground.
• Weight is a vector quantity and is expressed in Newton.
• Weight = Mass * gravitational acceleration

(1) Gravitational acceleration of moon is one-sixth of gravitational acceleration on earth.

g = $\frac{1}{6} *9.8=1.63 m/s^{2}$

(2) Weight on moon = Mass of person on moon * gravitational acceleration of moon

110.84 = mass on moon * 1.63

Mass of person on moon = 68 kg

(3) Weight of person on earth = mass of person * 9.8

Mass of any object remains constant in the universe, so mass of the person on earth = mass on moon = 68 kg

Weight on earth = 68 * 9.8 = 666.4 Newton

Answer:

(1) 'g' on moon = 1.63 $m/s^{2}$.

(2) Mass of person on moon = 68 kg

(3) Weight on earth = 68 * 9.8 = 666.4 Newton