Question

If the weight of the body is 1000 dyne, then the mass of the body will be
(A) \[{10^{ - 1}}kg\]
(B) \[{10^{ - 2}}kg\]
(C) \[{10^{ - 3}}kg\]
(D) \[{10^{ - 4}}kg\]

Answer 1

Hint Weight is actually the force generated by the body on earth. Quantitatively, it is the mass times the acceleration due to gravity of the planet on which the mass is placed. In this question we are given the force in terms of dynes. We first need to convert it into the SI units which is N and then proceed further by dividing the weight by the acceleration due to gravity. This will give us the mass of the body.

Complete step by step solution
We are given force in terms of dynes or in the CGS system. The SI unit of force is N which is kg \[\dfrac{m}{{{s^2}}}\] . We need to convert each unit to its counterpart in the CGS system. As we know that 1kg = 1000g and 1m = 100cm, Therefore.
 \[\dfrac{{1kg \times m}}{{{s^2}}} = \dfrac{{1000g \times 100cm}}{{{s^2}}}\]
 \[
  \Rightarrow \dfrac{{1 kg \times m}}{{{s^2}}} = {10^5}\dfrac{{g \times cm}}{{{s^2}}} \\
  \Rightarrow 1N = {10^5}dynes \\
  \Rightarrow 1dyne = {10^{ - 5}}N \\
 \]
Therefore 1000 dynes will be equal to \[{10^{ - 2}}N\] . Now we will find the mass of the body from this force.
 \[
  W = mg \\
  \Rightarrow {10^{ - 2}} = m \times 10 \\
  \Rightarrow {10^{ - 3}} = m \\
 \]

Therefore, the answer with the correct option is option C.

Note
The weight of the body is subject to the acceleration due to gravity of that planet. This acceleration due to gravity is affected by the mass and radius of the planet on which the body is kept. However weight is a universal quantity and its value will remain the same whatever the external conditions be.