Question

When a solid moves therough a liquid, the liquid opposes the miotioon with a force F. The magnitude of F depends on the coefficient of viscosity `eta` of the liquid, the radius r of the sphere aknd the speed v of the sphere. Assuming that F is proportional to different powers of these quantities, guess a formula for F using the method of dimension.

Answer 1

Suppose the formula is `F=keta^a r^b v^c`.
Then, `MLT^-2=[ML^-1T^-1]^aL^b(L/T)^c`
`=M^aL^-(a+b+c) T^(-a-c)`
Equating the exponents of M,L and T from both sides, `
` a=1`
` -a+b+c=1`
` -a-c=-2`
Solving these `a=, b=1, and c=1.`
solving these `a=1, b=1, and c=1`.
Thus, the formula for `f is `F=Ketarv`.