If the length of a simple pendulum is halved, then its energy becomes

Options

A. double
B. half
C. 4 times of the initial
D. 3 times of the initial

Answer

A

Explanation

For the simple pendulum,
Total energy `=(1)/(2) m omega^(2)A^(2)`
`therefore E=(1)/(2)m (4pi^(2))/(T^(2)) A^(2) i.e. E prop (1)/(T^(2))`
But `T=2pisqrt((l)/(g)) therefore T^(2)=(4pi^(2)l)/(g) i.e. T^(2) prop l`
`therefore E prop (1)/(l)`
`therefore (E_(2))/(E_(1))=(l_(1))/(l_(2))=(2l_(2))/(l_(2))=2`
`therefore E_(2)=2E_(1) therefore` If l is halved, the energy is doubled.