Question

As in the figure, a uniform sphere of mass = 0.84 kg and radius r = 4.2 cm is supported by a string (of negligible mass) attached to a wall (whose friction can also be ignored). The center of the sphere is a vertical distance L = 10 cm below the attachment point of the string. Find the tension in the string. (Note that the direction of the tension (along the string) is along a line passing through the center of the sphere.)

Your answer should be in N, but enter only the numerical part in the box.

Answer 1

given
L = 10 cm
r = 4.2 cm
m = 0.84 kg
let theta is the angle made by the string with vertical.

from fig, theta = tan^-1(r/L)

= tan^-1(4.2/10)

= 22.8 degrees

let T is the tension in the string.

as the sphere is in equilibrium, net force acting on it must be zero.

Apply, Fnety = 0

T*cos(theta) - m*g = 0

T*cos(theta) = m*g

T = m*g/cos(theta)

= 0.84*9.8/cos(22.8)

= 8.93 N <<<<<<<<<----------------------Answer