(Solved):   (a)Determine the moment of inertia of the semiellipsoid with respect to the \( x \) axis a ...

 

(a)Determine the moment of inertia of the semiellipsoid with respect to the \( x \) axis and express the result in terms of the mass \( m \) of the semiellipsoid. The material has a constant density \( \rho \). (05marks) (b) The pendulum consists of two slender rods \( A B \) and \( O C \) which have a mass of \( 3 \mathrm{~kg} / \mathrm{m} \). The thin circular plate has a mass of \( 12 \mathrm{~kg} / \mathrm{m}^{2} \). Determine the moment of inertia of the pendulum about an axis perpendicular to the page and passing through the point at \( O \). (05 marks) (c) The mountain bike has a mass of \( 40 \mathrm{~kg} \) with center of mass at point \( G_{1} \), while the rider has a a mass of \( 60 \mathrm{~kg} \) with center of mass at point \( G_{2} \). When the brake is applied to the front wheel, it causes the bike to decelerate at a constant rate of \( 3 \mathrm{~m} / \mathrm{s}^{2} \). Determine the normal reaction the road exerts on the front and rear wheels. Assume that the rear wheel is free to roll. (10marks)