1) A hollow sphere and a solid sphere of the same mass and radius each roll up i

Question

1) A hollow sphere and a solid sphere of the same mass and radius each roll up in incline without slipping. Each is given the same initial translational speed, and each begins at the same height. Which rolls furthest up the incline?

a) Solid sphere

b) Hollow sphere

c) Neither (both reach the same height

2) A planet moves in an elliptical orbit around the Sun such that its distance of closest approach to the Sun is one third that of its furthest distance. What is the ratio of speeds (vcolsest / vfurthest)?

a) 9 b)3 c)1 d)1/3 e)1/9

3) Two identical masses m are placed at opposite corners of a square with sides of length L. What is the magnitude of the gravitational potential energies (Uclosest / Ufurthest)?

Explain your answer please

Explanation / Answer

ans 1

Solid sphere = 2/5 * m * r^2 = 0.4 * m * r^2
Hollow sphere = * m * r^2 = 0.667 * m * r^2

If there is no friction, these circular objects will SLIDE down the inclined plane at the acceleration and finish the race at the same time.

theren is no roll of ineria

ans 2

by Keplers second law v1 d1 = v2 d2

let d1=d than d2=3d

ans 3:1= Vclose:Vfurt

partc

U=-Gmm/L

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