An ellipse with semi major axis 'a' semi minor 'b' revolving in uniform magnetic field'B'. Find value of average of joule heating (resistance =R)

An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency omega , the average power loss in the loop due to Joule heating is :

Distance of center of mass from point O by lamda R/pi for uniform semi ring. Find value of lamda

A liquid is filled into a semi eliiptical cross section with a as semi major axis and b as semi minor axis. The rato of surface tension forces on the curved part and the plane part of the tube in vertical position will be