A simple pendulum with length 100cm and bob of mass 250g is...

From the given figure we can see that

$sin{\theta}_{0} = \dfrac{A}{l} = \dfrac{10}{100} = \dfrac{1}{10}$

From conservation of energy $\dfrac{m{v}^{2}}{2} = mgl ( 1 - cos{\theta}_{0} )$

Maximum tension occurs at mean position

$T = mg + \dfrac{m{v}^{2}}{l} ⇒ T = mg + 2mg ( 1 - cos{\theta}_{0} )$

Substituting the values,

$T = mg ( 1 + 2 ( 1 - \sqrt{1 - \sin^{2}{\theta}_{0}} ) ⇒ T = mg ( 3 - 2\sqrt{1 - \dfrac{1}{100}} ) ⇒ T = 0 . 25 \times 9 . 8 ( 3 - 2 ( 1 - \dfrac{1}{200} ) ) ⇒ T = 0 . 25 \times 9 . 8 \times 1 . 01 = 2 . 4745N$

It is given that

$T = \dfrac{x}{40} ⇒ x = 40 \times 2 . 4745 = 98 . 98 \approx 99$