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Q.

In a hypothetical set of units, mass, acceleration and frequency are taken as fundamental units. If unit of mass is 100 g, unit of acceleration is 2 m/s2 and unit of frequency is 4 sec-1 in the new system of units then find the value of one joule in this system.

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answer is 40.

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Detailed Solution

Energy ∝ mxayfzML2T−2=[M]xLT−2yT−1z1=x2=y−2=−2y−z⇒z=−2 Energy ∝ma2f21.0J=xJ′x=(1.0)JJ′=(1.0)M1M21a1a22f1f2−2=(1.0)1kg100g1m/s22m/s221sec−14sec−1−2=(1.0)(10)14(16)=40
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