91影视

The tensions at mass $m$with velocity $v$and radius$r$of circular motion $T_{a}to{T}_d$

Centripetal force equal to tension acting on the string.

The free-body diagram shows that the downward gravitational force is balanced by an upward component of the tension, leaving the radial component of the tension to cause the centripetal acceleration. Newton鈥檚 second law is

$\underset{}{鈭�}{F}_r=T=\frac{m{v}^2}{r}$

The above tension equation is applied for the given cases of free body diagram of FIGURE Q8.3

case (a): The tension at mass m with velocity v and radius of circular motion gives

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

case (b): The tension at mass m with velocity v and radius of circular motion gives

$T_b=\frac{m{v}^2}{2r}=0.5\frac{m{v}^2}{r}$

case (c): The tension at mass m with velocity v and radius of circular motion gives

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

case (d): The tension at mass m with velocity v and radius of circular motion gives

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

The Tensions of each string for different cases are ranked in the order

$T_c>T_b>T_d=T_a$