Question

Force of gravity on a mass of $ 15{\text{kg}} $ on the surface of a planet is $ 25{\text{N}} $ . Find acceleration due to gravity due to this planet.

Answer 1

Hint : To solve this question, we need to use Newton's second law of motion for the free fall of the mass on the planet. Then, equating with the value of the force of gravity given in the question, we can get the final answer.

Formula Used: The formula which is used to solve this question is given by
 $\Rightarrow F = ma $ , here $ F $ is the force acting on a body of mass $ m $ which is moving with an acceleration of $ a $ .

Complete step by step answer
Let the acceleration due to gravity due to this planet be $ a $ .
Let us consider the free fall of the mass on this planet. If the mass is allowed to fall freely on the surface of this planet, then it will fall with the acceleration equal to the acceleration due to this gravity. We know from Newton’s second law of motion that the mass of a body is related to its acceleration by the relation
 $\Rightarrow F = ma $
According to the question, we have $ m = 15kg $ . So we get
 $\Rightarrow F = 15a $ ……………………….(i)
The force of gravity on this planet is given to be equal to $ 25{\text{N}} $ . Therefore we have
 $\Rightarrow F = 25 $ ………………………...(ii)
Equating (i) and (ii) we have
 $\Rightarrow 15a = 25 $
Dividing by $ 15 $ on both the sides we get
 $\Rightarrow a = \dfrac{{25}}{{15}} $
 $ \Rightarrow a = 1.67m/{s^2} $
Hence, the acceleration due to gravity due to this planet is equal to $ 1.67m/{s^2} $ .

Note
The force of gravity experienced by a body on the surface of a planet is known as its weight on that planet. Due to the variation of the acceleration due to gravity on each planet, the weight of a body is different on each planet. It must be noted that the mass is a constant for each body on any planet.