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A calorie is a unit of heat or energy an...

A calorie is a unit of heat or energy and it equals about `4.2 J, where 1 J = 1 kg m^(2) s^(-2)`. Suppose we employ a system of units in which the unit of mass equals `alpha kg`, the unit of length equals is `beta m` , the unit of time is `gamma s`. Show tthat a calorie has a magnitude `4.2 alpha^(-1) beta^(-1) gamma^(2)` in terms of the new units.

Text Solution

Verified by Experts

`n_(2)=n_(1)[(M_(1))/(M_(2))]^(a)((L_(1))/(L_(2)))^(b)((T_(1))/(T_(2)))^(c)`
`=4.2((kg)/(alphakg))^(1)((m)/(betam))^(2)((s)/(gammas))^(-2)`
`n_(2)=4.2alpha^(-1)beta^(-2)gamma^(2)`
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Knowledge Check

  • Imagine a system of units in which the unit of mass is 100 kg, length is 1 km and time is 1 minute Then 1 joule in this system is equal to

    A
    360
    B
    3.6
    C
    `36xx10^5`
    D
    `36xx10^(-6)`

  • kg m^(2) s^(-2) represents the unit of

    A
    kinetic energy only
    B
    work done only
    C
    potential energy only
    D
    all the above

  • If mass is measured in unit of alpha kg, length in beta m and time in gamma s, then calorie would be

    A
    `4 2 alpha beta^(2)gamma^(-2)`
    B
    `[MT^(-2)]`
    C
    `42alpha^(-1)beta^(-2)gamma^(-2)`
    D
    `42alpha^(-2)beta^(-2)gamma^(-2)`

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