Question

Check the correctness of the following equation , a=v^2/r, where a=acceleration, v=velocity, r= radius

Answer 1

Answer:

hope my answer helps you.......

Answer 2

Answer:

The equation is correct dimensionally.

Explanation:

Given equation is

$a=\dfrac{v^2}r$

• $a$ = acceleration.

• $v$ = velocity.

• $r$ = radius.

The acceleration has units of $m/s^2$, therefore its dimensions are $[M^0L^1T^{-2}]$.

The velocity has units of $m/s$, therefore its dimensions are $[M^0L^1T^{-1}]$.

The radius has units of $m$, therefore its dimensions are $[M^0L^1T^0]$.

Dimensions of the RHS of the given equation is given by

$\dfrac{[v^2]}{[r]}=\dfrac{[M^0L^1T^{-1}]^2}{[M^0L^1T^0]} = \dfrac{[M^0L^2T^{-2}]}{[M^0L^1T^0]} = [M^0L^{2-1}T^{-2-0}]=[M^0L^1T^{-2}]$

which is dimensionally equal to the LHS of the given equation.

Thus, the equation is dimensionally correct.

This equation is representing the centripetal acceleration of a particle, moving in a circular path of radius $r$ with velocity $v$.