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If mass is measured in unit of alpha kg,...

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

`4.2 alpha^(-1) beta^(2) gamma^(2)`

C

`4.2 alpha^(-1) beta^(-2) gamma^(2)`

D

`4.2 alpha^(-2) beta^(-1) gamma^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`4.2 alpha^(-1) beta^(-2) gamma^(2)`
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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 ?

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement system and others do not understands it. Instead of taking 1kg, 1m and 1 sec, as basic unit they took unit of mass as alpha kg , the unit of length as beta m and unit of times as gamma second. They called power in new system as ACME then match the two columns. {:(,"Column-I",,"Column-II"),((a),"1N in new system",(p),alpha^(-1) beta^(-2) gamma^(2)),((b),"1J in new system",(q),alpha^(-1) beta^(-1) gamma^(2)),((c),"1 pascal (SI unit of pressure) in new system",(r),alpha^(-1)beta gamma^(2)),((d),alpha "ACME in watt",(s),alpha^(2) beta^(2) gamma^(-3)):}

Suppose two students trying to make a new measurement system so that they can use it like a code measurement system and others do not understand it Instead of taking 1 kg, 1 m and 1 second, as basic unit they took unit of mass as alpha kg, the unit of length as beta m and unit of times as gamma second. They called power in new system as "Aakash", then find The value of alpha "Aakash" in watt.

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement. Instead of taking 1 kg, 1 m 1 s, as the basic unit they took unit of mass as alpha kg, the unit of length as beta m and the unit of tme as gamma s. They called the new system as ACME. Column I represents the units of the physical quantities, Column II represents the ACME units and Column III represents the CGS units of the physical quantities. Which of the following represents the correct combination for a physical quantity known as rate of energy?

What is the unit of alpha, beta , gamma ?

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.

If units of length, mass and force are chosen as fundamental units, the dimensions of time would be :

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