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Q.

A calorie is a unit of heat and equals 4.2 J. Suppose we employ a system of units in which the unit of mass is α  kg, the unit of length is β  metre and the unit of time is γ  s.In this new system, 1 calorie =

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a

4.2  α−1β−2γ2

b

4.2  αβ2γ−2

c

αβ2γ2

d

α−1β−2γ2

answer is D.

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Detailed Solution

[Calorie]=[ML2T−2]

Comparing with general dimensional formula [MaLbTc], we get a =1, b = 2, c = 2

n2=4.2  [1  kgα  kg]1[1  mβ  m]2[1  sγ  s]−2=4.2  α−1β−2γ2

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