An oscillating pendulum has a velocity of 2ms-1 at the equilibrium position O and velocity at same point P. Using the diagram above, calculate the height of...

An oscillating pendulum has a velocity of 2ms^-1 at the equilibrium position O and velocity at same point P. Using the diagram above, calculate the height of P above O. (Take g = 10ms²)

Answer Details

To solve this problem, we need to use the conservation of mechanical energy of the pendulum. At the highest point P, the pendulum is momentarily at rest, and all its kinetic energy has been converted to potential energy. Therefore, the sum of kinetic and potential energies at P is equal to the sum of kinetic and potential energies at O. At position O, the pendulum has only kinetic energy, which is given by the formula 1/2 * m * v^2, where m is the mass of the pendulum and v is its velocity. We are not given the mass of the pendulum, but we can assume that it is constant throughout the motion. Therefore, the kinetic energy at O is 1/2 * m * (2)^2 = 2m. At position P, the pendulum has only potential energy, which is given by the formula m * g * h, where h is the height of P above O. Therefore, the potential energy at P is m * g * h. Since the total mechanical energy of the pendulum is conserved, we can equate the kinetic energy at O to the potential energy at P: 2m = m * g * h Simplifying this equation, we get: h = 2 / g = 2 / 10 = 0.2m Therefore, the height of P above O is 0.2m. Answer option (D) is correct.