Question

22. Which of the following have the same dimensions as v2/r where v is the speed of the particle describing a circular path of radius r. * O (a) area O (b) force O (c) acceleration O (d) volume​

Answer 1

v²/r has same dimensions as that of ACCELERATION.

But how ?

LHS :

$\rm \bigg \{ \dfrac{ {v}^{2} }{r} \bigg \}$

$\rm = \bigg \{ \dfrac{ {(L{T}^{ - 1} )}^{2} }{L} \bigg \}$

$\rm = \bigg \{ L{T}^{ - 2} \bigg \}$

$\rm = \bigg \{ \dfrac{L{T}^{ - 1}}{T} \bigg \}$

$\rm = \bigg \{ \dfrac{Velocity}{Time} \bigg \}$

$\rm = \bigg \{Acceleration \bigg \}$

$\rm = \: RHS$

So v²/r has same dimensions of acceleration.

OPTION C) IS CORRECT ✔️