20) Four particles each of mass m are placed at the corners of a square of side length l - Physics - System Of Particles And Rotational Motion

Question

20) Four particles each of mass m are placed at the corners of a
square of side length l The radius of gyration of the system about
an axis perpendicular to the square and passing through centre
is
(1) l2√(2) l2(3) l(4) l2√

Vaibhav T. · Accepted Answer

Dear Student,

Let K be the radius of gyrationAC=BDAC=l2+l2=l2AO=CO=BO=DOAO=l22=l2Moment of inertia of the given lamina about an axis passing through O and perpendicular to the lamina,I=m×l22+m×l22+m×l22+m×l22I=4m×l22I=2ml2  
 1Also, I=mK2  
 2compare 1 and 2, we get,K2=2l2K=l2

20) Four particles each of mass m are placed at the corners of a square of side length l. The radius of gyration of the system about an axis perpendicular to the square and passing through centre is .(1) l2√(2) l2(3) l(4) l2√

20) Four particles each of mass m are placed at the corners of a square of side length l. The radius of gyration of the system about an axis perpendicular to the square and passing through centre is .
(1) l2√(2) l2(3) l(4) l2√