Question

a particle is moving with a constantbspeed v along a circular path of radius r the magnitude of change in velocity between two diametrically opposite points is 1. 2V 2. root 2V 3. v/2 4.zero​

Answer 1

Step-by-step explanation:

We know change in velocity can also be called as acceleration.

We know the formula of acceleration

$a = \frac{final \: velocity \: - initial \: velocity}{time \: taken}$

$here \: final \: velocity \: and \: initial \: velocity \: is \: same \: = v \: \\ total \: time \: taken \: = t$

$a = \frac{v - ( - v)}{t1}$

$a = \frac{2v}{t1}$

$as \: it \: is \: moving \: in \: a \: circular \: path \: so \: time \: taken \: is \: \frac{2\pi \: r}{v}$

$t 2= \frac{2\pi \: r}{v}$

$\frac{t2}{2} = \frac{\pi \: r}{v}$

$since \: t1 = \frac{t2}{2}$

$so \: we \: have \: a = \frac{ 2v}{ \frac{\pi \: r}{v} }$

$= > a = \frac{2 {v}^{2} }{\pi \: r}$