Question

If in a system the force of attraction between two-point masses of $1kg$ each situated $1km$ apart is taken as a unit force and is called notwen (newton written in reverse order) and if $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$ in SI units, the relation of notwen and newton is:

• A. $1\text{notwen}=6.67\times {10}^{-11}\text{newton}$
• B. $1\text{notwen}=6.67\times {10}^{-19}\text{newton}$
• C. $1\text{notwen}=6.67\times {10}^{-12}\text{newton}$
• D. $1\text{notwen}=6.67\times {10}^{-17}\text{newton}$

Answer 1

The correct option is D $1\text{notwen}=6.67\times {10}^{-17}\text{newton}$

As we know,
If two-point masses each of masses $1kg$ are separated a distance $1m$ they experience a force $6.67\times {10}^{-11}\text{newton.}$
$F=G\frac{m_1{m}_2}{r^2}$
Hence,
$1\text{notwen}=6.67\times {10}^{-11}\times \frac{(1kg{)}^2}{(1km{)}^2}$
$1km={10}^{3}m$
Therefore,
$1\text{notwen}=6.67\times {10}^{-11}\times {10}^{-6}\frac{(1kg{)}^2}{(1m{)}^2}$
$1\text{notwen}=6.67\times {10}^{-11}\times {10}^{-6}\text{newton}$
$1\text{notwen}=6.67\times {10}^{-17}\text{newton}$