1. Q6. A satellite orbits the Earth in a circular orbit with radius r and speed v . Suppose the orbiting
radius is increased by a factor of 2, in order to stay in a stable orbit the orbiting speed must
A. (2)^(1/2) v
B. v /(2)^(1/2)
C. v /2
D. 2 v
E. Remain the same
Q7. A circular cylinder with mass of 1 kg and radius a=0.1 m is rotating about its cylindrical axis
at a rate of 5 revolutions per second. It is then placed on a flat surface. Assuming that there is no
dissipation at contact and the cylinder is rolling without slipping (with negligible rolling friction)
on the flat surface, its translational speed is
A.    3.14 m/sec
B.    2.53 m/sec
C.    2.22 m/sec
D.    1.81 m/sec
E.    1.41 m/sec
Solution
orbital speed V^2 = GM/R
here R is the radius of the earth
so

2. V2^2/V^2 = R1/R2
V2^2/V^2 = R/2R = 1/2
V2 = [v /(2)^(1/2)]
Option (b) is correct.
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