Q52 / 57 · KVPY 2019 (SA) · Physics

A water-proof laser pointer of length 10 cm placed in a water tank rotates about a horizontal axis passing through its centre of mass in a vertical plane as shown in the figure. The time period of rotation is 60 s. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to (Take, refractive index of water =133 )

Figure

 

  • A
     8.13 s
     
  • B
    14.05 s
     
  • Correct answer
    C
    16.67 s
     
  • D
    23.86 s

Solution

When angle of incidence of laser on surface of water is less than critical incidence, it goes out otherwise reflected back into the tank.

Figure

For water, ic=sin-11n=sin-111.33
⇒ic=sin-1(0.75)
⇒ic≈50°
If ω= angular speed and t= time to travel an arc of 2ic, then using ωt=2ic. We have, t=2icω
=2×50180×π2π60=16.67 s

Hence, the correct answer is option: 'C'.

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