Question

In a practical unit if the unit of mass becomes double and that of unit of time becomes half, then $8$ joule will be equal to ............. unit of work.

• A. 6
• B. 4
• C. 1
• D. 10

Answer 1

Answer: (C)

Work $\rightarrow\left[ ML ^{2} T ^{-2}\right]$
$n_{1} v_{1}=n_{2} v_{2}$
$\frac{(8) M_{1} L_{1}^{2} T_{1}^{-2}}{M_{2} L_{2}^{2} T_{2}^{-2}}=n_{2}$
$\Rightarrow 8\left[\frac{M_{1}}{M_{2}}\right]\left[\frac{L_{1}}{L_{2}}\right]^{2}\left[\frac{T_{1}}{T_{2}}\right]^{-2}=n_{2}$
$\Rightarrow 8\left[\frac{M_{1}}{2 M_{1}}\right]\left[\frac{L_{1}}{L_{1}}\right]^{2}\left[\frac{2 T_{1}}{T_{1}}\right]^{-2}=n_{2}$
$\Rightarrow 8 \times \frac{1}{2} \times \frac{1}{4}=n_{2}$
$\Rightarrow n_{2}=1$
So, unit of $8$ joule $=1 \times$ new units