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Q.

In a new system 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 the value of 0.1 J in this system is

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answer is 4.

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Detailed Solution

Energy ∝mxayfzML2T−2=[M]xLT−2yT−1z1=x2=y−2=−2y−z⇒ z=−2 Energy ∝ma2f20.1J=xJ′x=(0.1)JJ′=(0.1)M1M21a1a22f1f2−2=(0.1)1kg100g1m/s22m/s221sec−14sec−1−2=(0.1)(10)14(16)=4
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In a new system 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 the value of 0.1 J in this system is