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 $$_______$$

[ Energy ]$$=ML2T$$−$$2=ML2T$$−$$4T2=MLT-22T-2=Ma2f2$$, $$a-$$ acceleration and $$f-$$ $$frequencyn1u1=n2u2$$⇒$$n2=101kg0.1kg1m/s22m/s22$$×$$sec$$−$$14sec$$−$$1$$−$$2$$⇒$$n2=10$$×$$10$$×$$14$$×$$16$$⇒$$n2=400$$

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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 _______

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

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Physical quantities and units

Remember concepts with our Masterclasses.

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 _______

[ Energy ]=ML2T−2=ML2T−4T2=MLT-22T-2=Ma2f2, a- acceleration and f- frequencyn1u1=n2u2⇒n2=101kg0.1kg1m/s22m/s22×sec−14sec−1−2⇒n2=10×10×14×16⇒n2=400

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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 _______