A simple pendulum consists of a 50 cm long string attached to a 100...

Given $m = 100 \text{ g} = 0.1 \text{ kg}$, $L = 50 \text{ cm} = 0.5 \text{ m}$, and \theta = 37^{}^{{}^{\circ}}.

The height descended by the bob from its initial position to the lowest point is:

h = L - L \cos \theta = L(1 - \cos 37^{}^{{}^{\circ}})

Substituting the values, we get:

$h = 0.5 \times \left(1 - \dfrac{4}{5}\right) = 0.5 \times 0.2 = 0.1 \text{ m}$

Using the principle of conservation of mechanical energy, the velocity $v$ at the lowest point is given by:

$\dfrac{1}{2}mv^2 = mgh \Rightarrow v^2 = 2gh$

Taking $g = 10 \text{ m/s}^2$, we have:

$v^2 = 2 \times 10 \times 0.1 = 2 \text{ m}^2/\text{s}^2$

At the lowest position, the net force towards the center provides the necessary centripetal acceleration:

$T - mg = \dfrac{mv^2}{L}$

$T = mg + \dfrac{mv^2}{L}$

Substituting the known values into the equation:

$T = (0.1 \times 10) + \dfrac{0.1 \times 2}{0.5}$

$T = 1.0 + 0.4 = 1.4 \text{ N}$