The moment of inertia of a body about a given axis is 12   kg   m 2 . Initially the body is at…

The moment of inertia of a body about a given axis is 12 kg m2. Initially the body is at rest. In order to produce a rotational kinetic energy of 15000 J, an angular acceleration of 10 rad s-2 must be applied about that axis for a duration of________.
  1. 2 s
  2. 4 s
  3. 10 s
  4. 5 s

Solution

The kinetic energy of rotation is,

K.E.=12Iω2=12×12×ω2=15000 Jω2=15000 J12×12=3000012⇒ω=3000012=50 rad s-1

Using the equation of motion of rotation,

ω=ω0+αt50=0+10×tt=5 s

Asked in: AP EAMCET 2018 (25 Apr Shift 1)

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