First slide

Physical quantities and units

Question

In a new system of units, unit of mass is 100 g, unit of acceleration is 2 m/s² and unit of frequency is 4 sec^-1, in this new system of units, then the value of 10 J in this new system is _______

Moderate

Solution

$\begin{array}{l} [Energy] = M L^{2} T^{- 2} = M L^{2} T^{- 4} T^{2} = \frac{M {(L T^{- 2})}^{2}}{T^{- 2}} = \frac{M a^{2}}{f^{2}}, a - a c c e l e r a t i o n a n d f - f r e q u e n c y \\ n_{1} u_{1} = n_{2} u_{2} \\ \Rightarrow n_{2} = 10 [\frac{1 kg}{0.1 kg}] {[\frac{1 m / s^{2}}{2 m / s^{2}}]}^{2} \times {[\frac{\sec^{- 1}}{4 \sec^{- 1}}]}^{- 2} \\ \Rightarrow n_{2} = 10 \times 10 \times \frac{1}{4} \times 16 \\ \Rightarrow n_{2} = 400 \end{array}$

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