The ball weighing 10 kg is attached to a string and rotated in a circular path that has a radius of 10 m. The ball completes 10 rotations per second or the angular velocity is 10*2*pi radians/sec.
The linear velocity of the ball is v = 10*10*2*pi m/s
The kinetic energy of the ball is 10*(10*10*2*pi)^2/10
When the ball is brought closer to 5 m away from the center, the kinetic energy of the ball is 10*(10*10*2*pi)^2/5
The increase in kinetic energy is the work that is required. This is given by
10*(10*10*2*pi)^2/5 - 10*(10*10*2*pi)^2/10
=> 10*(10*10*2*pi)^2*(1/5 - 1/10)
=> 10*(10*10*2*pi)^2/10
=> (10*10*2*pi)^2
=> 4*pi^2*10^4
=> 125.6 kJ
The work required to pull the ball closer while it rotates at the same speed is 125.6 kJ
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