Question

The force F on a sphere of radius a moving in a medium with velocity v is given by F=6πnav. The dimension of n are
a) [ML^-3]
b) [MLT^-2]
c)[MT^-1]
d) [ML ^-1T^-1]​

Answer 1

$\huge{\bold{\underline{\underline{Solution:-}}}}$

$\large{\bold{\underline{To \: Find}}}$

Dimensions of n = ?.

$\large{\bold{\underline{\underline{Step - by - Step - Explanation}}}}$

The formula given is F = 6πnav.

Dimensions of :-

${F = M L T^{-2}}$

${a = L}$

${v = L T^{-1}}$

${n }$ = ?.

6 and π are constants and are dimension less.

Substituting the above values in the Force formula.

${M L T^{-2} = n \times L \times L T^{-1}}$

${M L T ^{-2} = n \times L^{2} T^{-1}}$

$\large{n = \frac{M L T^{-2}}{L^{2}T^{-1}}}$

${n = M L^{-1} T^{-1}}$

$\huge{\boxed{\boxed{n = M L^{-1} T^{-1}}}}$

So,the dimensions of n is $\bold{M L^{-1} T^{-1}}$ (option-4).

Answer 2

Answer:

OPTION d is correct

hope it helps