Question

If the unit of length is doubled and that of mass and time is halved, the unit of energy will be :

• A. doubled
• B. $4$ times
• C. $8$ times
• D. same

Answer 1

Answer: (C)

$8$ times

$E=\frac{M{L}^2}{T^2}$
$L^{{}^{\prime }}=2L$
$M^{{}^{\prime }}=M/2$
$T^{{}^{\prime }}=T/2$
$E^{{}^{\prime }}=\frac{M^{\prime }{L}^{\prime {}^2}}{T^{\prime 2}}=M/2\times \frac{{\left(2L\right)}^2}{{\left(T/2\right)}^2}=8\left(\frac{M{L}^2}{T^2}\right)=8E$