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If unit of mass is taken as 1 kg, of tim...

If unit of mass is taken as 1 kg, of time a 1 minute and that acceleration due to gravity is taken as `9.81 ms^(-2)` . What is the unit of energy?

Text Solution

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New unit of energy `=E_1`
New unit of mass `M_(1) = 1 kg`
New unit of time `T_(1) = 1 "minute" = 60 "sec"`
New unit of length `= L_(1)`
`E_(1) = [M_(1) L_(1) T_(1)^(-2) ]`
New unit of acceleration due to gravity,
`g_(1) = 9.81 ms^(-2)`
`g_(1) = L_(1)T_(1) ^(-2) L_(1) = g_(1) T_(1)^(-2) = 9.81 xx (60)^(2) "meter" `
`E_(1) = [ 1 kg xx (9.81 xx 60^(2) )^(2) m^(2) (60)^(-2) S^(-2) ]`
`E_(1) = (1 xx 9.81 xx 60 xx 60 xx 9.81 xx 60 xx 60)/( 60 xx 60) "kgm"^(2) s^(2)`
`E_(1) = 3.464 xx 10^(5) "kg" m^(2) sec^(-2)`
`therefore` The new unit of energy `E_(1) = 3.464 xx 10^(5)` joule.
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