Question

Check following are correct or not:
1kgf m = 10Nm (nearly)
1 gf cm = 1000 dyne cm (nearly)

Answer 1

In this question we required to prove that the left-hand side is equal to the right-hand side in both expressions by using acceleration due to gravity that is $g=10m/{{s}^{2}}$. kg represents kilograms and f represents force. Similarly, g represents grams. Convert them into their respective values in one unit system to prove.

Complete step-by-step solution
We know that in the first case the left-hand side is given by 1kgfm
One kilogram-force is the force due to gravity on a mass of 1kg. Therefore, 1kgf = force due to gravity on a mass of 1 kg.
So, 1kgf = mass 1kg $\times$ acceleration due to gravity (g)
As we know ‘g’ is constant having value $10m/{{s}^{2}}$
$\begin{aligned} & 1kgf=1kg\times 10m/{{s}^{2}} \\\ & 1kgf=10kgm/{{s}^{2}} \\\ \end{aligned}$
Multiplying m on both sides we get
$\begin{aligned} & 1kgf\times m=10kgm/{{s}^{2}}\times m \\\ & As,kgm/{{s}^{2}}=N \\\ \end{aligned}$
Put in above equation
So, $1kgf\times m=10Nm$
Now take the second equation and prove it 1gf cm is the same as the above equation but it has a unit of C.G.S system. In this case, we have to calculate the value of acceleration due to gravity (g) in $cm/{{s}^{2}}$ that is
$\begin{aligned} & g=1000cm/{{s}^{2}} \\\ & 1gfcm=1g\times 1000cm/{{s}^{2}}\times cm \\\ & 1gfcm=1000gcm/{{s}^{2}}\times cm \\\ \end{aligned}$
As we know in C.G.S system,
$gcm/{{s}^{2}}=dyne$
Now put this in above equation we get,
$1gfcm=1000dyne\text{ }cm$
It is proved that 1kg fm = 10Nm and 1gf cm = 1000 dyne cm.

Note: g is the acceleration due to gravity $g=10m/{{s}^{2}}$ as well as $g=1000cm/{{s}^{2}}$ we have to clearly use these two values of gravity according to the given units. We need to remember the units in the SI and C.G.S system to solve this question. Because units are different in both C.G.S and SI systems of units.