KCET2014PhysicsRay Optics
A body having a moment of inertia about its axis of rotation equal to ( 3 ~kg ~m ² ) is rotating with angular velocity of ( 3 rad s⁻¹ ). Kinetic energy of this rotating body is same as that of a body of mass ( 27 ~kg ) moving with velocity ( v ). The value of ( v ) is
Options
- A( 1 ~ms ⁻¹ )
- B( 0.5 ~ms ⁻¹ )
- CO ( 2 ~ms ⁻¹ )
- D( 1.5 ~ms ⁻¹ )
Correct answer
A. ( 1 ~ms ⁻¹ )
Step-by-step solution
Given, moment of Inertia, ( I=3 kgm ² ); angular velocity, ( =3 rads ⁻¹ ; ) mass,, ( m =27 ~kg ) Now ( 1 2 m v²= 1 2 I ² ) ( m v²=I ² v²= I ² m ) Therefore, ( v= I m ) Substituting the values, we get ( v= 3 27 3= 1 9 3= 1 3 3 ) Thus, velocity of body is ( 1 ~ms ⁻¹ )