Question

Two skaters, each of mass 70 kg, skate at speeds of 4 m/s in opposite directions along parallel lines 1.5 m apart. As they are about to pass one another they join hands and go into circular path about their common centre of mass. Angular velocity of their motion is :

• A. 5.3 radian/second
• B. 2.7 radian/second
• C. 2.0 radian/second
• D. 1.2 radian/second

Answer 1

Answer: (D)

1.2 radian/second

Answer 2

COM of the system must be equal to 70 cm from left end of the bottom most metre stick for maximum value of x for maintaining equilibrium. If COM is on right side of the edge then torque of gravitational force of the system would produce rotational motion about edge.

Taking O as origin X_CM(max) = 70 cm

Using $\mathrm { X } _ { \mathrm { CM } } = \frac { \mathrm { m } _ { 1 } \mathrm { x } _ { 1 } + \mathrm { m } _ { 2 } \mathrm { x } _ { 2 } + \mathrm { m } _ { 3 } \mathrm { x } _ { 3 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } + \mathrm { m } _ { 3 } }$

$70 \mathrm {~cm} = \frac { \mathrm { m } \cdot ( 50 \mathrm {~cm} ) + \mathrm { m } ( 50 + 10 ) \mathrm { cm } + \mathrm { m } ( \mathrm { x } - 30 + 50 ) \mathrm { cm } } { 3 \mathrm {~m} }$

210 m = 50 m + 60 m + 20 m + mx

x = 80 m