In a new unit system, 1unit of mass\=0.25kg, 1unit of length\=0.1m, 1unit of time\=0.5s. What is 3J (1J\=1kg m2s−2) in t
\[J\]=\[M L2T−2\]. 3J=3kg×(1m)2×(1s)−2=3×(4×0.25)×(10×0.1)2×(2×0.5)−2=3×1×1×4=12new units. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that 12 new is correct because its dimensions and unit match the physical quantity asked.
Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae