The resistive force F acting on a ball of radius r moving with velocity v is given by F=K r v The dimensional formula of K is

Question

The resistive force F acting on a ball of radius r moving with velocity v is given by F=K r v The dimensional formula of K is (A) [MLT] (B) [ M -1 LT ] (C) [ M -1 L -1 T ] (D) [ ML -1 T -1]

Tardigrade Admin · Accepted Answer

As F=K r v [K]=([F]/[r][v])=( MLT -2/ LLT -1)= ML -1 T -1

Q. The resistive force $F$ acting on a ball of radius $r$ moving with velocity $v$ is given by
$F = Kr v$
The dimensional formula of $K$ is

$[M L T]$

$[M^{- 1} L T]$

$[M^{- 1} L^{- 1} T]$

$[M L^{- 1} T^{- 1}]$

As $F = Kr v$
$[K] = \frac{[ F ]}{[ r ] [ v ]} = \frac{M L T ^{- 2}}{LL T ^{- 1}} = M L^{- 1} T^{- 1}$

Q. The resistive force F acting on a ball of radius r moving with velocity v is given by F=Krv The dimensional formula of K is

[MLT]

[M−1LT]

[M−1L−1T]

[ML−1T−1]