A barbell consists of a 500g ball and a 2.0 Kg ball connected by a massless 50-c

Question

A barbell consists of a 500g ball and a 2.0 Kg ball connected by a massless 50-cm-long rod Where is the center of mass X_cm with respect to the center of the heavier mass m_1? (a) 0.50 m (b) 0.40 m (c) 0.30 m (d) 0.20 m (e) 0.10m (f) none of these What is the speed of the 2.0-Kg ball if they rotate about the center of mass at 40 rpm? (a) 41.9 m/s (b) 1.76 m/s (c) 0.42 m/s (d) 0.04 m/s (e) none of these What is the speed of the 500-g ball if they rotate about the center of mass at 40 rpm? (a) 10.5 m/s (b) 7.02 m/s (c) 1.68 m/s (d) 0.67 m/s (e) none of these

Explanation / Answer

5) for the center of mass ,

taking 2 Kg as origin

position of m1 = 0 m

position of m2 = 0.50 m

for the center of mass = (2 * 0 + 0.50 * 0.50)/(2 + 0.50)

center of mass = 0.10 m = 10 cm

the correct option is e) 0.10 m
6)

as w = 40 rpm = 40 * 2pi/60 rad/s

w = 4.2 rad/s

speed of 2 Kg object = x * w

speed of 2 Kg object = 0.10 * 4.2

speed of 2 Kg object = 0.42 m/s

the correct option is c) 0.42 m/s

7)

for the 500 gm bal
speed of 0.50 Kg object = (0.50 - 0.10) * 4.2

speed of 0.50 Kg object = 1.68 m/s

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