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 $\to \left[M{L}^2{T}^{-2}\right]$
$n_1{v}_1=n_2{v}_2$
$\frac{(8)M_1{L}_1^2{T}_1^{-2}}{M_2{L}_2^2{T}_2^{-2}}=n_2$
$\Rightarrow 8\left[\frac{M_1}{M_2}\right]{\left[\frac{L_1}{L_2}\right]}^2{\left[\frac{T_1}{T_2}\right]}^{-2}=n_2$
$\Rightarrow 8\left[\frac{M_1}{2M_1}\right]{\left[\frac{L_1}{L_1}\right]}^2{\left[\frac{2T_1}{T_1}\right]}^{-2}=n_2$
$\Rightarrow 8\times \frac{1}{2}\times \frac{1}{4}=n_2$
$\Rightarrow n_2=1$
So, unit of $8$ joule $=1\times$ new units