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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

Verified by Experts

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

  • In a new system of units, unit of mass is 10 kg, unit of length is 1 km and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is

    A
    `3.6 xx 10^(-4)` new units
    B
    `6 xx 10^(7)` new units
    C
    `10^(11)` new units
    D
    `1.67 xx 10^(4)` new units

  • 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?

    A
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    B
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    C
    (II) (i) (M)
    D
    (I) (iv) (K)