Question

9. To find the conversion factor between the units of the force in two
different system of units.
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Answer 1

mainly, there are three different type of measurement systems

MKS , CGS and FPS

in MKS , unit of force is same as unit of force in SI system. i.e., Newton.

now let's converse unit of force MKS system to CGS system.

using formula, $n_1D_1=n_2D_2$

here, n1 = 1, D1 = (1kg)(1m)/(1s)²

n2 = ?, D2 = (1g)(1cm)/(1s)²

we know, 1g = 10^-3 kg, 1cm = 10^-2 m

so, 1 × (1kg)(1m)/(1s)² = n2 × (10^-3kg)(10^-2m)/(1s)²

or, 1 × (1kg)(1m)/(1s)² = n2 × 10^-5 × (1kg)(1m)/(1s)²

or, 1 = n2 × 10^-5

or, 10^5 = n2

hence, 1 N = 10^5 gcm/s² or 10^5 Dyne [ as Unit of force in Cgs is Dyne ]

again, conversion of force in FPS system.

similarly, n1D1 = n2D2

here, n1 = 1, D1 = (1kg)(1m)/(1s)²

n2 = ?, D2 = (1lb)(1ft)/(1s)²

[ we know, 1 lb = 0.454 kg , 1ft = 0.3048m]

= (0.454 kg)(0.3048m)/(1s²)

= 0.1383792 (1kg)(1m)/(1s)²

so, 1 × (1kg)(1m)/(1s)² = n2 × 0.1383792 (1kg)(1m)/(1s)²

or, n2 = 1/0.1383792 = 7.2265

hence, 1N = 7.2265 lb.ft/s² ≈ 7.223 lb.ft/s²