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- What is the work done by a force of $1gf$ in displacing a body of $5g$ through $1cm$?Take $g = 10m/{s^2}$.

Last updated date: 13th Jun 2024
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Hint: In this question, we have to change the gram force into newton. After that we can use the formula of work done and substitute the values of force and displacement.

Complete step by step solution:
According to the question, we have given $1gf$ which is equal to the $0.01N$when $g = 10m/{s^2}$. So, $1gf = 0.01N$.
Now, again from the question, the mass of the body $m = 5g$ and the displacement caused by the force $F = 1gf$ or $F = 0.01N$ is $d = 1cm$ or $d = 0.01m$(as $1cm = 0.01m$). So, the work done $W$ on the body is given as-
$W = F \bullet d$
  W = 0.01 \times 0.01 \\
   \Rightarrow W = 0.0001kgm/s \\
   \Rightarrow W = 0.0001J \\
Hence, the work done by a force of $1gf$ in displacing a body of $5g$ through $1cm$ is $0.0001J$.

Additional Information: We know that the unit of force is ‘newton’ but in this question, a new unit is used for force which is $gf$. The full form of $gf$ is ‘gram force’. It is also known as ‘g-force’. One-gram force is equal to the product of one gram of mass and standard acceleration due to gravity of earth. The standard acceleration of earth is equal to $9.80665m/{s^2}$.

Note: We have to remember that the unit of work in the MKS system is Joule which is equal to kgm/s. But in the question, we have the force in gram force. So, first we have to change it into newton. The standard value of $1gf$ is $0.00980665N$ when $g = 9.80665m/{s^2}$ but we have given that $g = 10m/{s^2}$. So, the value of $1gf$ is equal to $0.01N$. In the question, we have the mass of the body but it is not to be included into the calculations.