Question

The mass and weight of an object on earth are $ 5kg\text{? 49N} $ respectively. What will be their value on the moon? Assume that the acceleration due to gravity on the moon is $ {{\dfrac{1}{6}}^{th}} $ of that on the earth.

Answer 1

Hint :Mass will remain constant on earth and moon as it is a constant quantity.
 $ W=mg $
Where $ W $ is weight, $ m $ is mass, $ g $ is acceleration due to gravity.

Complete Step By Step Answer:
Given data
 $ m=5kg $
 $ {{W}_{e}}= $ Weight on earth $ =49N $
 $ {{g}_{m}} $ i.e. gravity of moon, $ {{g}_{e}} $ acceleration due to gravity on earth.
 $ {{g}_{m}}=\dfrac{1}{6}{{g}_{e}} $
We know that,
 $ W=mg $
 $ {{W}_{e}}=m{{g}_{e}} $
 $ 49=5\times {{g}_{e}} $
 $ {{g}_{e}}=9.8\text{ m/}{{\text{s}}^{2}} $
According to the relation given,
 $ {{g}_{m}}=\dfrac{1}{6}{{g}_{e}}=\dfrac{1}{6}\times 9.8 $
 $ {{g}_{m}}=1.633\text{ m/}{{\text{s}}^{2}} $
 $ \therefore $ Weight on moon $ =m{{g}_{m}} $
 $ =5\times 1.633 $
 $ =8.166\text{ N} $

Additional Information:
Although the moon is Earth’s only natural satellite, there are a number of near Earth objects with orbits that are in resonance with earth. These have been called the second moon of earth. The first manmade object to reach the moon was the Soviet Union Luna $ 2 $ unscrewed spacecraft in $ 1959. $ United states NASA Apollo Program, which conducted the first manned lunar orbiting mission with Apollo $ 8 $ in $ 1968. $ six human leading from $ 1969 $ to $ 1972. $ These missions returned lunar rocks which have been used to develop a detailed geological understanding of the moon’s origins, internal structure and subsequent history. The most widely accepted origin explanation posits. That the moon formed about $ 4.51 $ billion years ago not long after Earth.

Note :
Mass of an object is the measure of an object's inertial property. The weight of an object is a measure of the force exerted on the object by near the earth or another aestival body is attracted towards the centre of the body by gravity.
An object weight depends on its mass and the strength of the gravitational pull. The moon orbits Earth at an average lunar distance of $ 384400\text{ km}\text{.} $ Moon is a differential lucky body has a surface gravity of $ 0.1654g $
About one sixth of Earth’s and lacks a significant atmosphere, hydrosphere or magnetic field.
On average the distance from Earth to the Moon is about $ 238,855 $ miles. The Earth is $ 3.67 $ times the diameter of the moon.