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  4. If the unit of length, mass and time each is doubled, the unit of work is increased by:

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Q. If the unit of length, mass and time each is doubled, the unit of work is increased by:

EAMCETEAMCET 1996

Solution:

The dimensional formula for work done is as $ W=[M{{L}^{2}}{{T}^{-2}}] $ Now, units M, L and T are doubled, then work done becomes $ W[2M]{{[2L]}^{2}}{{[2T]}^{2}} $ $ W=\frac{2\times 4}{4}\times [M{{L}^{2}}{{T}^{-2}}] $ $ W=2\times W $ Hence, unit of work increases by 2 times.