Question

A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s. If the rim of the umbrella is a circle of 1 metre in diameter and the height of the rim above the floor is 1.5 m, the drops of water spun off the rim and hit the floor at a horizontal ______ m from the umbrella.

Options

• 0.872

• 0.829

• 0.789

• 0.456

Answer 1

A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s. If the rim of the umbrella is a circle of 1 metre in diameter and the height of the rim above the floor is 1.5 m, the drops of water spun off the rim and hit the floor at a horizontal 0.829 m from the umbrella.

Explanation:

Angular speed = ω = `21/44 "rps" = 21/44 xx 2pi`

∴ `v = omegaR = 21/22 pi xx 1/2 = (21pi)/44`

`[∵ "diameter" = 1, "radius" = 1/2]`

For the next part of the motion, using `s_y = 1/2 g t^2`

⇒ `1.5 = (9.8t^2)/2`

`t = sqrt(3/9.8)`

Now using s_x = u_x t = vt

`s_x = (21pi)/44 xx sqrt(3/9.8) = 0.829` m