A planet has four times the mass and half the escape velocity of Earth. How many times larger is the radius of that planet as compared to Earth? 

 

2. Four tennis balls, each of the same mass, are placed at positions 0 cm, 2 cm, 6 cm, and 14 cm along the x-axis. At what position on the x-axis is the center of mass of the four tennis balls located? 

 

3. Consider an elastic collision in one dimension between two particles. The second particle is initially at rest. After the collision, the two particles move in opposite directions and have the same speeds. If the mass of the first particle is 3 kg, what is the mass of the second particle? 

 

4. A bug is sitting on the outer edge of a ceiling fan, 110 cm away from the axis of rotation. The fan has an angular speed of 2 rad/s (radians per second). What is the magnitude of the centripetal acceleration of the bug? (in m/s²) 

 

5. A ceiling fan starts to spin from rest with a constant angular acceleration of 10 rad/s² (radians per second square). How many full rotations does the fan execute after 3 seconds? 

 

6. Two objects of masses m₁=3 kg and m₂=7 kg are able to slide without friction on the circular track shown in the figure. The track has a radius R=1m.
  Both objects are initially at rest. The right object (that of mass m₂) rests on the ground level. The left object (that of mass m₁), is released from an initial height of 1m above the ground level. It slides down and collides inelastically with the other object so that both objects stick together and move jointly with the same speed. What maximal height (in meters) above the ground level will the two objects reach?

Om m R