Question

Suppose A = B^xC^y, where the units in meters and seconds of A, B, C are respectively m.s, m2/s, and m.s2. Then the exponents x and y have the values:

A) 2/3 ; 1/3 B) 4/5 ; -1/5 C) 1/5 ; 3/5 D) 2 ; 3  

Answer 1

Given that

Unit of A = m.s

Unit of B = m^2/s

Unit of C = m.s^2

Now since in an equation unit on both side should be equal. Now given equation is

A = B^x*C^y

Unit of A = Unit of (B^x*C^y)

m.s = (m^2/s)^x*(m.s^2)^y

m.s = m^(2x)*s^(-x)*m^y*s^(2y)

m.s = m^(2x + y)*s^(2y -x)

now comparing both sides

m = m^(2x + y)

2x + y = 1

s = s^(2y - x)

2y - x = 1

Now we have 2 equation and 2 unknowns, So

2x + y = 1

2y - x = 1

Multiply with 2 to 2nd equation

2x + y = 1

4y - 2x = 2

Now add both equation

5y = 3

y = 3/5

x = 2y - 1

x = 2*(3/5) - 1 = 1/5

So,

x = 1/5 & y = 3/5

Corect option is C.

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