Question

A metal 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.

Answer 1

As it is given that 2 kg mass is suspended by 12 cm long thread and then a horizontal force is applied on it so that it remains in equilibrium at 30 degree angle

So here we can use force balance in X and Y directions

now for X direction or horizontal direction we can use

`F = Tsin30`

for vertical direction similarly we can say

`mg = T cos30`

so here we first divide the two equations

`(F)/(mg) = (sin 30)/(cos 30)`

`(F)/(mg) = tan 30`

`F = mg tan30`

now plug in all values in the above equation

`F = 2 * 9.8 * tan30`

`F = 11.3 N`

Part b)

now in order to find the tension in the thread we can use any above equation

`F = T sin30`

`11.3 = T sin30`

`T = (11.3)/(sin30)`

`T = 22.6 N`

so tension in the thread will be 22.6 N