The correct answer is option B) 79/81
Explanation::
Formula for tension in vertical circle along a string is \(T={mv^2\over r}+mg \cos\theta\)
For highest point \(\theta\) = \(π\)
\(\therefore T={mv^2\over r}-mg \)
For lowest point \(\theta =0\)
\(\therefore T={mv^2\over r}+mg\)
After simplification
Ratio =\(v^2-gr\over v^2+gr\)
Putting values 40 m/s^{2}, 10 m/s, 2m
\(={1600-20\over 1600+20}\)
\(={79\over81}\)