The correct answer is (A) 2.0 J
Total energy of the pendulum is the sum of its kinetic and potential energy. At the instant of time, when the pendulum is at a height h and has a speed v, Its energy is given by,
[tex]E=mgh+\frac{1}{2} mv^2[/tex]
Substitute 2.0 kg for m, the mass of the pendulum, 9.81 m/s² for g, the acceleration due to gravity, 0.10 m for h and 4.0 m/s for v.
[tex]E=mgh+\frac{1}{2} mv^2\\ =(2.0kg)(9.81m/s^2)(0.10 m)+\frac{1}{2}(2.0kg)(4.0m/s)^2\\ =17.962J[/tex]
The pendulum has an initial energy of 20 J. the energy lost is given by,
[tex]\Delta E=(20J)-(17.962J)\\ =2.038J=2.0J[/tex]
Thus, the energy lost by the pendulum is (A) 2.0 J
