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A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of (a) 1.0 m/s (b) 0.5 m/s (c) 1.5 m/s (d) 2.0 m/s

A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of
(a) 1.0 m/s (b) 0.5 m/s
(c) 1.5 m/s (d) 2.0 m/s

Grade:12

2 Answers

Arun
25763 Points
one year ago
Rotation of the body = 3 kg-m² (Given)
Angular velocity of the body = 3 rad/s (Given)
Weight of the mass = 27kg (Given)
Using the equation of motion -
1/2Iω² = 1/2mv²
Therefore, 1/2.3kgm². 3²rad/s = 1/2.27kgv²
= 1/2.3kgm². 9rad/s = 1/2.27kgv²
Thus v² = 1
Thus, the kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of 1.0m/s.
 
Vikas TU
14149 Points
one year ago
Rotational kinetic energy of the body is same as the translational kinetic energy of body of mass  27 kg 
1/2 Iw^2 = 1/2 mv^2 
1/2 *3 * 9 = 1/2 * 27 * v^2 
v = 1m/s

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