Question

A wooden ball of mass 10 g is suspended by a thread. The horizontal current of air blows it from one side so that so that thread makes an angle of 60 degrees with vertical. What is tension in thread and force of air current?

Answer 1

Tension `=0.049N`
Force due to air current `=0.042N`, rounded to three decimal places

Explanation:

As shown in the figure above, the ball of mass `m=10g` is in equilibrium. The three forces acting on the ball are

1. Weight `mg` acting downwards
2. Horizontal force `F` exerted by the air current
3. Tension `T` exerted by the thread making an angle of `θ=60^@` to the vertical.

Resolving `T` in its horizontal and vertical components respectively we get
`Tsin60^@=F` ......(1)
`Tcos60^@=mg` .....(2)

Taking `g=9.8ms^-2`, From (2)
`Txx1/2=10/1000xx9.8`
`=>T=10/1000xx9.8xx2=0.049N`

Inserting this value in (1)
`0.049xxsqrt3/2=F`
`=>F=0.042N`, rounded to three decimal places