Question

If the unit of mass is doubled, and the units of length and time are halved, how much is 20 N of force in new units? $(1N=1kgm{s}^{-2})$

• A. 0.5 N
• B. 5 new units of force
• C. 5 N
• D. 0.5 new units of force

Answer 1

The correct option is D 0.5 new units of force

Let the original unit of force, $F=20N=\left[ML{T}^{-2}\right]$
Let the new unit of force, length, mass and time be F', L', M', and T' respectively.
Given that, $L^{{}^{\prime }}=\frac{L}{2}$, $M^{{}^{\prime }}=2M$ and $T^{{}^{\prime }}=\frac{T}{2}$
The new unit of force, $F^{{}^{\prime }}=\left[M^{{}^{\prime }}{L}^{{}^{\prime }}{T}^{{}^{\prime }-2}\right]$
$\left[\right(2M\left)\left(\frac{L}{2}{\left(\frac{T}{2}\right)}^{-2}\right)\right]=4\left[ML{T}^{-2}\right]=4F=4\times 20=80N$
This is coming "0.5 new units of force".