For a particle executing SHM with an amplitude ‘r’, the kinetic energy will be equal to the potential energy when the displacement is equal to-

x = A sin w t           displacement in SHM

v = A w cos w t      velocity in SHM

PE = 1/2 k x^2 = 1/2 k A^2 sin^2 w t

KE = 1/2 m v^2 = 1/2 m w^2 A^2 cos^2 w t

If KE = PE then

k sin^2 w t = m w^2 cos^2 w t

sin^2 wt / cos^2 w t = tan^2 w t = m w^2 / k

but k / m = w^2

So tan^2 w t = 1  and tan w t = 1   or w t = pi / 4 or theta = 45 deg

Then  x = r sin w t  = r sin 45 = .707 r

answer: option c.

explanation:

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.