Question

Force acting on a particle is $5\, N$. If the units of length and time are doubled and unit of mass is halved, then numerical value of the force in the new system will be

• A. $5$
• B. $1/20$
• C. $20$
• D. $1/5$

Answer 1

Answer: (C)

$20$

Answer 2

$n_{2}=n_{1}\left(\frac{M_{1}}{M_{2}}\right)^{^1}\left(\frac{L_{1}}{L_{2}}\right)^{^1}\left(\frac{T_{1}}{T_{2}}\right)^{^{-2}}$ $=5\left(\frac{M_{1}}{M_{1} / 2}\right)\left(\frac{L_{1}}{2L_{1}}\right)\left(\frac{T_{1}}{2T_{1}}\right)^{^{-2}}$ $=20$