The amplitude of a simple pendulum is 10cm. When the pendulum is at a displacement of 4cm from the mean position, the ratio of kinetic and potential enegies at that point is,

Options

A. 5.25
B. 2.5
C. 4.5
D. 7.5

Answer

A

Explanation

The kinetic energy is given by `KE=(1)/(2)momega^(2)(A^(2)-x^(2))` while the potential energy is given by `PE=(1)/(2)momega^(2)x^(2)`.
Therefore the ratio, `(KE)/(PE)=((1)/(2)momega^(2)(A^(2)-x^(2)))/((1)/(2)momega^(2)x^(2))Rightarrow(KE)/(PE)=(A^(2)-x^(2))/(x^(2))`
`Rightarrow (10^(2)-4^(2))/(4^(2))=(84)/(16)Rightarrow(KE)/(PE)=(21)/(4)=5.25`