Question

A small container of water is placed on a carousel inside a microwave oven, at a radius of 13.5 cm from the center. The turntable rotates steadily, turning through one revolution each 7.15 s. What angle does the water surface make with the horizontal?

Answer 1

`\theta=0.607^(\circ)`

Step-by-step explanation:

Given that,

A small container of water is placed on a carousel inside a microwave oven, at a radius of 13.5 cm from the center, r = 13.5 cm

Time for each rotation, t = 7.15 s

To find,

Angle made by the water surface with the horizontal

Solution,

Two forces are acting on the water surface namely centripetal force and the force of gravity

The centripetal force is given by :

`F_c=mr\omega^2`

`F_c=mr((2\pi)/(T))^2`

`F_c=m13.5* 10^(-2)((2\pi)/(7.15))^2`...........(1)

The force of gravity is given by :

`F_g=m* g`

`F_g=m* 9.8`..............(2)

Let
`\theta` is the angle the water surface make with the horizontal. It can be calculated from equation (1) and (2) as :

`tan\theta=(F_c)/(F_g)`

`tan\theta=(m13.5* 10^(-2)((2\pi)/(7.15))^2)/(m* 9.8)`

`tan\theta=0.0106`

`\theta=0.607^(\circ)`

Therefore, this is the required solution.