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

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.

32: from largest to smallest, this hierarchy includes eons, eras, periods, epochs, and ages.

33: answer is c

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