1) A solid sphere of radius R and mass M is

held against a wall by a string being pulled at

an angle θ . f is the magnitude of the frictional

force and W = M g .Which of the following equations may be

derived from the fact that the torque about

point O must be 0?

1. F sin θ = f

2. F cos2

θ = f

3. F = f

4. W = f

5. F + W = f

6. F sin θ cos θ = f



2)Which of the following may be derivived from

the fact that the vertical component of force

must be 0?

1. F cos θ + W = f

2. F sin θ = f

3. F sin θ = f + W

4. F sin θ + f = W

5. F sin θ = W



3)Find the smallest coefficient of friction µ

needed for the wall to keep the sphere from

slipping.

1. µ =

1

cos θ

2. µ = sin θ

3. µ = tan θ

4. µ =

1

tan θ

5. µ = cos θ

6. µ =

1

sin θ