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A light , right rod is 40.0 cm long.Its ...

A light , right rod is `40.0 cm` long.Its top end is pivoted on a frictionless, horizontal axle. The rod hangs straight down at rest with a small , massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full cirle. What minimum speed at the bottom is required to make the ball go over the top of the circle?

A

`2.5 m//s`

B

`4.0 m//s`

C

`3.0 m//s`

D

`5.0 m//s`

Text Solution

Verified by Experts

The correct Answer is:
B
Consider energy conservation of the ball-Earth system beyween the instant just after you strike the ball and the instant when it reaches the rop . The speed as the top is zero if you hit it just hard enough to get it there.
`Delta K = Delta U = 0:`
`(0 - (1)/(2) mv_(i)^(2)) + [mg (2L) - 0] = 0`
`v_(i) = sqrt(4 gL) = sqrt(4 (10.0m//s^(2)) (0.40m))`
`v_(i) = 4.0 m//s`
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