Three objects, a hollow cylinder, spherical shell and solid cylinder are given t

Question

Three objects, a hollow cylinder, spherical shell and solid cylinder 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. 990 m/s B. 4.95 m/s C. 3.50 m/s D. 2.50 m/s E. 700 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)

Moment of inertia of hollow cylinder is I1 = mr2

Moment of inertia of spherical shell is I2 = (2/3) mr2

Moment of inertia of solid cylinder is I3 = (1/2) mr2

When the body reaches to maximum height on the inclined plane,

then Potential energy stored by body = change in its kinetic energy

mgh = (1/2) mv2 + (1/2) Iw2

angular velocity , w = v/r

For Hollow cylinder : mgh1 = (1/2) mv2 + (1/2) (mr2 ) (v/r)2 = mv2

h1 = (v2 /g) ------------(1)

For spherical shell : mgh3 = (1/2) mv2 + (1/2) ((2/3)mr2 ) (v/r)2 =(5/6) mv2

h2 = 0.83 (v2 /g) ------------(2)

For solid cylinder : mgh3 = (1/2) mv2 + (1/2) ((1/2)mr2 ) (v/r)2 =(3/4) mv2

h3 = 0.75 (v2 /g) ------------(3)

h1 > h2 >h3

Answer is A) Hollow sphere , Spherical shell , Spherical shell

4)

When the body reaches to maximum height on the inclined plane,

then Potential energy stored by body = change in its kinetic energy

mgh = (1/2) mv2 + (1/2) Iw2

5 x 9.81 x 5 = (1/2) 5 v2 + (1/2) (5 x 10-2 ) ( v2 / 0.12 )

5 x 9.81 x 5 = (5/2 ) v2 + (5/2 ) v2

v= 7.00m/s

Answer is E) 7.00 m/s

5)

moment of inertia I = 5 x 10-2 kg.m2

For hollow cylinder I = mr2 = 5 x (0.1)2 = 5 x 10-2 kg.m2

Answer is c) A hollow cylinder

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