A uniform rod, AB, of length 2m and mass 1kg, has a particle of mass 1kg attached to it at B. It can rotate freely about a horizontal axis through A. The end B is attached by means of an elastic string of natural length 1m to a point a distance 2m above A. The system is held at rest with AB horizontal and is then released. If the rod just reaches the vertical position, find the modulus of elasticity of the string.
I got the modulus of elasticity
λ=17.6. I first found the initial strain energy, which turned out to be
1.67λ. Kinetic and gravitation potential energies are initially 0J.
At the top when the rod is vertical, the kinetic energy and the strain energy are 0J. Let G be the centre of mass of the rod. It can be found that AG is 1.5m. Also the total mass of the rod and particle is 2kg. So at top, gravitational potential energy is 2*9.8*1.5 = 29.4. Equating
1.67λ=29.4 gives
λ=17.6. But the answer apparently is 10.4.
Where did I go wrong? Thank you for your help
.