Ametal ball of mass 2 kg is supported by a massless inextensible string, 12 cm long. a horizontal force displaces the ball by 30oto the vertical so that the string remains taut. find: a) the horizontal force. b) the tension in the thread.

(a) the horizontal force is 11.3 N

(b) The tension in the thread is 22.6 N

Draw a free body diagram for the suspended metal ball as shown in the figure. The tension T acts along the length of the thread, the force F is the horizontal force and its weight is mg, which acts vertically down wards.

Resolve the tension into two components- T cos 30 along the vertical and T sin30 along the horizontal as shown in the figure.

Apply the condition for equilibrium along the horizontal direction.

Apply the condition for equilibrium along the vertical direction.

Divide equation (1) by equation (2) and write an expression for F.

Substitute 2 kg for m and 9.81 m/s² for g.

The horizontal force required to keep the ball taut is 11.3 N

From equation (2),

Thus, the tension in the thread is 22.6 N

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