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

$\frac{F}{mg} = \frac{sin 30}{cos 30}$

$\frac{F}{mg} = tan 30$

$F = mg tan30$

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

$F = T sin30$

$11.3 = T sin30$

$T = \frac{11.3}{sin30}$

$T = 22.6 N$

so tension in the thread will be 22.6 N