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Question

A ring of M.I 102 kg/m2 about an axis passing through its centre and perpendicular to its plane is placed with its centre at origin. The current is passed through ring so that magnetic moment is M=(4^i3^j)Am2. When magnetic field B=(3^i+4^j) is switched on at t = 0, then
  1. Angular acceleration of the ring at t = 0 is 5000 rad/s2.
  2. Angular acceleration of the ring at t = 0 is 3000 rad/s2
  3. Maximum angular velocity of the ring is 100 rad/sec.
  4. Maximum angular velocity of the ring is 200 rad/sec


Solution

The correct options are
A Angular acceleration of the ring at t = 0 is 5000 rad/s2.
C Maximum angular velocity of the ring is 100 rad/sec.
τ=M×B=25^k(Nm)
M.I. about an axis passing through centre of mass and parallel to τ,I=1022(kg.m2)
α=τI=5000rad/s212Iω2=uiuf=MB cos 90(MB cos 90)ω=2MBI=100rad/sec

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