A uniform sphere of weight W and radius 5 cm is being held by a string as shown in the figure. The tension in the string will be :

Hypotenuse ($$H$$): The total distance from the wall attachment point to the center of the sphere is the length of the string plus the radius. $$H = 8\text{ cm} + 5\text{ cm} = 13\text{ cm}$$
Base ($$B$$): The horizontal distance from the wall to the center of the sphere is simply the radius. $$B = 5\text{ cm}$$
Vertical Height ($$V$$): Using the Pythagorean theorem: $$V = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12\text{ cm}$$

$$\cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{V}{H} = \frac{12}{13}$$

For vertical equilibrium, the vertical component of the tension must balance the weight: $$T \cos\theta = W$$

$$T \left( \frac{12}{13} \right) = W$$

$$T = \frac{13W}{12}$$