Question

If planks constant is h ,speed of light in vacuum v,and newtons gravitational force g,which combination has the dimension of length?

Answer 1

Answer:

$\sqrt{\frac{hv}{g}}$

Explanation:

Dimension of h= $Js =Nms=\frac{kgm*m*s}{s^2}=\frac{kgm^2}{s}=\frac{ML^2}{T}$

Dimension of v= L/T

Dimension of force = N= $\frac{kgm}{s^2}=\frac{ML}{T^2}$

Now,

$(h)^\alpha (v)^\beta (g)^z = L^1$

Putting the dimension in place of h,v and g we get three equations:

1. $\alpha +z=0$

2. $2\alpha +z+\beta =1$

3. $\beta +2z+\alpha=0$

Upon solving we get,

$\alpha =\beta =1/2\\z=-1/2$

So our answer is:

$\sqrt{\frac{hv}{g}}$

Hope it helped :D