Respuesta :
Answer:
[tex]\theta=0.607^{\circ}[/tex]
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 :
[tex]F_c=mr\omega^2[/tex]
[tex]F_c=mr(\dfrac{2\pi}{T})^2[/tex]
[tex]F_c=m13.5\times 10^{-2}(\dfrac{2\pi}{7.15})^2[/tex]...........(1)
The force of gravity is given by :
[tex]F_g=m\times g[/tex]
[tex]F_g=m\times 9.8[/tex]..............(2)
Let [tex]\theta[/tex] is the angle the water surface make with the horizontal. It can be calculated from equation (1) and (2) as :
[tex]tan\theta=\dfrac{F_c}{F_g}[/tex]
[tex]tan\theta=\dfrac{m13.5\times 10^{-2}(\dfrac{2\pi}{7.15})^2}{m\times 9.8}[/tex]
[tex]tan\theta=0.0106[/tex]
[tex]\theta=0.607^{\circ}[/tex]
Therefore, this is the required solution.
