Question

1 gf cm = N m = dyne cm

• A. $9.8$
• B. $9.8\times {10}^{-3}$
• C. $9.8\times {10}^{-5}$
• D. $980$

Answer 1

Answer: (C), (D)

$980$

$1\text{gf cm}={10}^{-3}\text{kgf cm}$ because $1\text{kgf}=1000\text{gf cm}={10}^3\text{gf cm}$
Also, $1\text{cm}=0.01\text{m}={10}^{-2}\text{m}$
$⟹1\text{gf cm}={10}^{-3}\times {10}^{-2}\text{kgf m}$
$⟹1\text{gf cm}={10}^{-5}\text{kgf m}$
$1\text{kgf}$ is the force exerted on a body of mass $1\text{kg}$ by the Earth.
$⟹1\text{kgf}=1\text{kg}\times 9.8{\text{m s}}^{-2}$
$=9.8{\text{kg m s}}^{-2}=9.8\text{N}$
$\therefore 1\text{gf cm}={10}^{-5}\text{kgf m}$
$=9.8\times {10}^{-5}\text{N m}$
$1\text{N m}={10}^7\text{dyne cm}$
$⟹9.8\times {10}^{-5}\text{N m}$
$=9.8\times {10}^{-5}\times {10}^7=980\text{dyne cm}$