91Ó°ÊÓ

The mass of the ball is $m=500\mathrm{g}$, we have to calculate the gravitational Force on the mass.

The gravitational force acting on a ball is:

$F=mg$

Where,

$g$is the acceleration due to gravity$=9.8m/s^2$

$m$is the mass of the ball$=0.5$

Therefore,

$F=0.5×9.8$

$F=4.90N$

The gravitational force acting on the ball is$4.90N$.

The velocity at the top is $v=4.0\mathrm{m}/\mathrm{s}$, and the length of the string is $l=102\mathrm{cm}=1.02\mathrm{m}$, we have to calculate the Tension of the string at this position.

The required tension in the string at the bottom position is:

$T=\frac{m{v}^2}{L}+mg$

Here,

$T=$Tension in the string

$v=$Velocity at the top

$m=$Mass of the ball

$L=$Length of the string

role="math" localid="1648314532264" $T=\frac{0.5×{\left(4\right)}^2}{102×{10}^{-2}}+0.5×9.8$

role="math" localid="1648314543571" $T=2.93N$

The tension in the string is $2.94N$.

The velocity of the ball at the bottom of the circle is $v^{\text{'}}=7.5\mathrm{m}/\mathrm{s}$, we have to calculate the tension of the string at the bottom.

To find the tension of the string, when the ball is at the bottom:

$T=mg+\frac{m{v}^2}{r}$

role="math" localid="1648315247523" $T=0.5×9.8+\frac{0.5×7.5^2}{1.02}$

$T=32.5N$

When the ball is at the top the tension in the string is $32.5N$