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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 ?

Text Solution

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Here, `M_1 =kg, L_1 = 1m, T_1 = 1 s, M_2 = alpha kg, L_2 = beta m and T_2 = lambda s, n_1 = 5J, n_2 ?`
for energy, `U = [M^1 L^2 T^9-2)]`
`As n_2 u_2 = n_1 u_1`
`n_2 = u_1((u_1)/(u_2)) = n_1((M_1)/(M_2))^1((L_1)/(L_2))^2 ((T_1)/(T_2))^(-2) = n_1((1)/(alpha))^1((1)/(beta))^2 ((1)/(lambda))^(-2) = (n_1 lambda^2)/(alpha beta^2) = (5 lambda^2)/(alpha beta ^2)` new units of energy.
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Knowledge Check

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