Question

The unit of Mass is $\alpha$ kg. The unit of length is $\beta$ metre and the unit of time is $\gamma$ second. The magnitude of calorie in the new system is:

[1 calorie $=$ 4.2 Joules]

• A. $4.2{\alpha }^1{\beta }^2{\gamma }^{-2}$ new units
• B. $4.2{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$ new units
• C. ${\alpha }^{-1}{\beta }^{-2}{\gamma }^2$ new units
• D. $\frac{1}{4.2}{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$ new units

Answer 1

The correct option is A $4.2{\alpha }^1{\beta }^2{\gamma }^{-2}$ new units

Given that unit of mass $=\alpha$

unit of length $=\beta$

time $=\gamma$

as Unit of work = Joule

$Work=force\times displacement$

$=mass\times acceleration\times displacement$

as Unit of acceleration $=\frac{length}{(time{)}^2}$

Unit of displacement =length

$\Rightarrow Joule=mass\times \frac{length}{(time{)}^2}\times length$

$=\alpha {\beta }^2{y}^{-2}$

as $1cal=4.2Joule$

$\Rightarrow calorie=4.2\times Joule$

$1cal=4.2J$

$=4.2\times \left(\alpha {\beta }^2{\gamma }^{-2}\right)$

$\Rightarrow$ Unit of calorie $=4.2\left(\alpha {\beta }^2{\gamma }^{-2}\right)$