Assertion: In a simpleharmonic motion the kinetic and potential energy becomes equal when the displacement is `(1)/(sqrt(2))` time the amplitude
Reason: is `SHM` kinetic energy is zero when potential energy is maximum

Options

A. If both assertion and reason are true and the reasopn is correct explanation of the assertion
B. If both assertion and reason are true and but not the correct explanation of assertion
C. If assertion is true but the reason is false
D. If both assertion and reason are false

Answer

B

Explanation

From the relation potential energy of `SHM` is given
`as PE = (1)/(2) m omega^(2)y^(2)`
`andKE = (1)/(2)m omega^(2)(A^(2) - y^(2))`
Where `y` is the displacement and `A` is the amplitude by the condition `KE = PE`
`(1)/(2)m omega^(2)(A^(2) - y^(2)) = (1)/(2) m omega^(2)y^(2)`
`rArr m omega^(2)y^(2)A^(2)`
`rArr y = (1)/(sqrt(2))momega^(2)A^(2)`
Also we know that total energy is
`K = KE + PE`
Hence in `PE` is maximum then `KE` will be zero