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cylinder and a hoop have the same mass and radius. They are released at the same time and roll down a ramp without slipping.

1)Which one reaches the bottom first?
Cylinder
Hoop
Both reach the bottom at the same time

Respuesta :

Answer:

Explanation:

acceleration of a body rolling down an inclined surface with inclination θ

a = gsinθ / (1 + k² / r²)

Here k is radius of gyration of the body rolling down and r is the radius of it.

For hoop

k = r

a  = gsinθ / (1 + r² / r²)

= g / 2 x sinθ

0.5 gsinθ

For cylinder

k² =  r² /2

a  = gsinθ / (1 + r² /2 r²)

= 2 / 3 g sinθ

= .67 g sinθ

So acceleration is more for cylinder

Hence cylinder  will reach the bottom first.

1. The cylinder will reach the bottom first.

Calculation of the acceleration:

Here the body acceleration should be rolled down the inclined surface

So, the following equation should be used.

a = gsinθ / (1 + k² / r²)

Here

k is the radius of gyration

and r is the radius

Now

For hoop

k = r

a  = gsinθ / (1 + r² / r²)

= g / 2 x sinθ

0.5 gsinθ

For cylinder

k² =  r² /2

a  = gsinθ / (1 + r² /2 r²)

= 2 / 3 g sinθ

= .67 g sinθ

We can see that the acceleration is more for the cylinder.

Learn more about acceleration here: https://brainly.com/question/20371554

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