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A new system of units is proposed in wh...

A new system of units is proposed in which unit of mass is `alpha kg,` unit of length `beta` m and unit of time `lambda s.` How much will 5 J measure in this new system ?

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To solve the problem of converting 5 Joules into the new system of units defined by `alpha kg` for mass, `beta m` for length, and `lambda s` for time, we will follow these steps: ### Step 1: Understand the dimensional formula of energy The energy (in Joules) has a dimensional formula given by: \[ [E] = M L^2 T^{-2} \] where \(M\) is mass, \(L\) is length, and \(T\) is time. ...
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If the unit of mass is alpha kg, the unit of length is beta metre and the unit of time is " gamma ' second, The magnitude of calorie in the new system is (1 Cal = 4.23)

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

Knowledge Check

  • A new system of units is proposed in which unit of mass is alpha kg, unit of length beta m and unit of time gamma s. How much will 5 J measure in this new system ?

    A
    `5alphabeta^(2)gamma^(-2)`
    B
    `5alpha^(-1)beta^(-2)gamma^(2)`
    C
    `5alpha^(-2)beta^(-1)gamma^(-2)`
    D
    `5alpha^(-1)beta^(2)gamma^(2)`

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