In a hypothetical set of units, net force applied on a block of mass 10 kg moving with acceleration 10 m/s2 is given as 100 unit of force. When the same block is moving at a speed of 20 m/s its kinetic energy is 20 unit of energy. A liquid has a surface tension of 10 SI units. If the numerical value of surface tension of the liquid in new system of units is N, find the value of N. (Dimensional formula of surface tension is ML0T−2)
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Detailed Solution
Let in new system, dimensions be M', L' and T'∴ Given 100 M', L'T'−2=100MLT−2 …(i)20 M', L'2T'−2=20×100 ML2T−2 ….(ii)Solving (i) and (ii);∴ M'T'−2=1100MT−2∴ 10 surface tension MT−2 in SI unit =103M'T'−2 (new units)