A particle of mass m moves with constant speed v on a circular path of radius r as shown in figure. The average force on it during its motion from A to B is

Question

A particle of mass m moves with constant speed v on a circular path of radius r as shown in figure. The average force on it during its motion from A to B is (A) (√3 m v2/2 π r) (B) (m v2/r) (C) (2 √3 m v2/π r) (D) (3 √3 m v2/4 π r)

Tardigrade Admin · Accepted Answer

F =m a=(m Δ v/Δ t)=[(2 v2 sin θ / 2/r θ)] =m[(2 v2 sin (2 π-2 π / 3)/r ⋅((4 π)3))] =(3 √3 m v2/4 π r)

Q. A particle of mass $m$ moves with constant speed $v$ on a circular path of radius $r$ as shown in figure. The average force on it during its motion from $A$ to $B$ is

$\frac{3 m v ^{2}}{2 π r}$

$\frac{m v ^{2}}{r}$

$\frac{2 3 m v ^{2}}{π r}$

$\frac{3 3 m v ^{2}}{4 π r}$

$F = ma = \frac{m Δ v}{Δ t} = [\frac{2 v ^{2} s i n θ /2}{r θ}]$
$= m [\frac{2 v ^{2} s i n ( 2 π - 2 π /3 )}{r \cdot ( \frac{4 π}{3} )}]$
$= \frac{3 3 m v ^{2}}{4 π r}$

Q. A particle of mass m moves with constant speed v on a circular path of radius r as shown in figure. The average force on it during its motion from A to B is

2πr3​mv2​

rmv2​

πr23​mv2​

4πr33​mv2​