You're on an asteroid with a gold sphere, and you need to determine if it is hollow or solid. You don't know the local value of g, but you have some precision tools with you. First, you attach a 32 cm string to make a simple pendulum with the sphere, and measure a period of 1.257 seconds. Next, you roll the sphere down an incline that starts at a height of 90 cm, and measure it to have a center-mass velocity of 2.94 m/s at the bottom of the incline. Is the sphere solid, or hollow? [Note: the results of Example 10.5 "Race of the rolling bodies" in the textbook will be helpfull.] Example 10.5 Race of the rolling bodies In a physics demonstration, an instructor "races" various bodies that roll without slipping from rest down an inclined plane (Fig. 10.16). What shape should a body have to reach the bottom of the incline first? SOLUTION IDENTIFY and SET UP: 1cm= CMR2 em EXECUTE: K₁ + U₁= K₂ + U₂ 0 + Migh - Much + R²(cm)² + 0 Mgh (1 + c)Muc 2gh Ucm √1 + € 1 EVALUATE: Shape solid sphere solid cylinder hollow sphere hollow cylinder C 2/5 1/2 2/3 1
