Three objects, a hollow cylinder, a spherical shell and a solid cylinder sphere

Question

Three objects, a hollow cylinder, a spherical shell and a solid cylinder sphere are given the same initial speed up a no-slip incline. Rank from highst to least high, the maximum height they reach. A. Hollow Cylinder, Spherical Shell, Solid Cylinder B. Spherical Shell, Solid Cylinder, Hollow Cylinder C. Solid Cylinder, Hollow Cylinder, Spherical Shell D. Spherical Shell, Hollow Cylinder, Solid Cylinder E. Solid Cylinder, Spherical Shell, Hollow Cylinder A rolling object is moving on a no-slip surface, assuming the moment of inertia is 5.00 times 10^-2 kgm^2, the radius is 10.0cm and the mass is 5.00kg, find the minimun speed it must have to roll over an obstacle of height 5.00m. A. 9.90 m/s B. 4.95 m/s C. 3.50 m/s D. 2.50 m/s E 7.00 m/s In the previous question, the shape of the object is most likely a A. A solid cylinder B A solid sphere C. A hollow cylinder D. A spherical shell E. A disk

Explanation / Answer

[3] ans

the velocity V=[2gh/1+B]^1/2

hollow cylinder =B=2/3

spherical shell=B=1/2

solid cylinder B=2/5

now we find the which object reach maximum height

H=(1+B)v^2/2g

hallow cylinder =>H=(1+2/3)v^2/2g=5v^2/6g=0.83v^2/g

spherical shell=(1+1/2)v^2/2g=3v^2/4g=0.75v^2/g

solid cylinder =(1+2/5)v^2/2g=7v^2/10g=0.7v^2/g

so the rank oder is

hallow cylinder,spherical shell,solid cylinder

the correct option is A

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4 ans

Given that

moment of inertia I=5*10^-2 kg*m^2

mass m=5 kg

radius r=0.1 m

height h=5 m

K^2=*5*10^-2/5=10^-2

B=k^2/R^2=10^-2/10*10^-2=0.1

now we find the minimum speed to roll down the obsaticle

the minimum speed V=[2gh/1+B]^1/2

=[2*9.8*5/1+0.1]^1/2

=9.9 m/s

the correct option is A

the shape of the object is solid cylinder

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