A tennis ball on a string is being swung in a horizontal circle of radius r. The ball has mass m and the string length l. Which expression gives the magnitude of the tension T in the string in terms only of the speed v of the ball and of m, r, and l?

Question

Answer choices
1. T=mgr/l
2. T=0, as is always the case for a conical pendulum.
3. T=mv^2/l
4. T=mv^2/r
5. T=m[g−(v^2/r)]
6. T=mv^2/2
7. T=mg
8. T=m[g+(v^2/r)]
9. T=mv^2l/r^2

Answer 1

I do not see where the length of the string (l) comes in the picture if the radius of the circular motion is fixed at r.

If the ball is swung in air where it is allowed to sag, then there is the horizontal component equal to mv²/r and the vertical component equal to mg.
The vectorial sum is
m*sqrt(g²+(v²/r)²)
which does not correspond to any of the options listed, unless the square-root sign (√) is missing from choices 5 and 8.

Answer 2

Actual Answer is 9

SA's answer of 4 is false, I tried it out personally, it doesn't work