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The time it takes for Betty's ball to hit the pins is .... that for Barney's ball to hit. *less than*

The time it takes for Wilma's ball to hit the pins is .... that for Fred's ball to hit. *greater than*

The time it takes for Barney's ball to hit the pins is .... that for Wilma's ball to hit. *greater than*

The time it takes for Betty's ball to hit the pins is .... that for Wilma's ball to hit. *less than*

The time it takes for Betty's ball to hit the pins is .... that for Fred's ball to hit. *equal*

The time it takes for Fred's ball to hit the pins is .... that for Barney's ball to hit *less than*

Here's what I did to solve the problem. First I found the moment of inertia for all of the balls. I used masses of 2 kg for the bigger ones, and 1 kg for the smaller ones. The radiuses I used were also 2 and 1 m for bigger & smaller balls.

Fred- (2/5)MR^2 = (2/5)(2)(2^2)= 3.2 kgm^2

Betty- (2/5)MR^2= (2/5)(1)(1^2)= .4 kgm^2

Barney- MR^2= (2)(2^2)= 8 kgm^2

Wilma- MR^2= (1)(1^2)= 1 kgm^2

I then used conservation of energy to find the velocity

[tex] mgH= (1/2)mv^2 + (1/2)I \omega^2 [/tex]

Solving for v gave me: [tex] \sqrt 2mgh/ m+ (I/R^2) [/tex]

I then plugged in my moments of inertia to get the velocities for the balls.

Fred's= 11.8 m/s

Betty= 11.8 m/s

Barney= 8.08 m/s

Wilma= 9.90 m/s

Then I compared the velocities to see which ball would get to the bottom faster, but not all of them are right. Can someone help me? Thanks.