Statement I: In a simple harmonic motion the kinetic and potential energies become equal when the displacement is $\frac{1}{\sqrt{2}}$ times the amplitude.
Statement II: In SHM kinetic energy is zero when potential energy is maximum.

Easy

A

If both statement I and statement II are true and statement II is the correct explanation of statement I.
B

If both statement I and statement II are true but statement II is not the correct explanation of statement I.
C

If statement I is true but statement II is false
D

If both statement I and statement II are false

Solution

From the relation, potential energy of SHM is given as $PE = \frac{1}{2} {mω}^{2} y^{2}$ and KE = $\frac{1}{2} {mω}^{2} (A^{2} - y^{2})$
where y is the displacement and A is the amplitufde
By the condition KE = PE
$\frac{1}{2} {mω}^{2} (A^{2} - y^{2}) = \frac{1}{2} {mω}^{2} y^{2}$
$\Rightarrow m ω^{2} y^{2} = \frac{1}{2} m ω^{2} A^{2}$
$\Rightarrow y = \frac{A}{\sqrt{2}}$
Also we know that total energy is $E = KE + PE$
Hence, if PE is maximum then KE will be zero.

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