First Challenge Problem on Scholar: I don't see how the solution gains the algebraic expressions, see solution link below, from the dimension expression i.e. 0 = v and 1 = -2x. Could someone please explain this to me.

http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/introduction-to-mechanics/units-and-dimensional-analysis/MIT8_01SC_problems01_soln.pdf

Question

First Challenge Problem on Scholar: I don't see how the solution gains the algebraic expressions, see solution link below, from the dimension expression i.e. 0 = v and 1 = -2x. Could someone please explain this to me.

http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/introduction-to-mechanics/units-and-dimensional-analysis/MIT8_01SC_problems01_soln.pdf

sidsiddhartha · Answer

yes
u can write the expression as
$$\large [M]^0[L]^0[T]^1=[ML^{-3}]^V*[L]^W*[LT^{-2}]^X*[L^2]^Y[L^2]^Z$$
ok???

sidsiddhartha · Answer

i've just written 
T as $$\large [M]^0[L]^0[T]^1$$

sidsiddhartha · Answer

do u get it? @samuelbird

sidsiddhartha · Answer

now add up the coefficients of M ,L and T
$$\large [M]^0[L]^0[T]^1=[M]^V*[L]^{-3V+W+X+2(Y+Z)}*[T]^{-2X}$$

sidsiddhartha · Answer

now if u compare coefficients from both sides then u'll get
$$V=0$$
$$-3V+W+X+2(Y+Z)=0$$
and
$$-2X=1$$
ok ???

sidsiddhartha · Answer

got this @samuelbird ?

anonymous · Answer

Yes, thanks a lot. That is a lot clearer now and seems like it should have been easy.

goformit100 · Answer

Hello, and A Warm Welcome to Open Study!