MHT CET 2017 :: Physics :: General questions

• Physics - General questions

The equation of the progressive wave is   $y= 3sin \left[ \pi\left(\frac{t}{3}-\frac{x}{5}\right)+\frac{\pi}{4}\right]$, where x and y are in metre and time in second .Which of the following is correct?

Answer:

Explanation:

 Compare the given equation with the  standard  equation of wave motion,

   $Y= A \sin\left[2\pi\left(\frac{t}{T}-\frac{x}{\lambda}\right)\times\frac{\pi}{4}\right]$

where, A  and $\lambda$ are amplitude and wave length respectively

 Amplitude , A= 3m

Wavelength , $\lambda$ =10 m

A wheel of moment of inertia 2 kg m² is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad/s. Due to friction, it comes to rest in 5 minutes. The  angular momentum of the wheel three minutes before  it slops rotating is 

Answer:

Explanation:

Given , l= 2 kg m²

 $\omega_{0}$ = 60 rad/s , $\omega$ =0

 t=5 min=5 x60= 300 s

 From the relation, 

$\omega=\omega_{0}+\alpha t$

$\alpha=\frac{\omega-\omega_{0}}{t}$

 $\Rightarrow $   $\alpha=\frac{0-60}{300}=\frac{-60}{300}=\frac{-1}{5}rad/s^{2}$

 for t=2 min

 = 2 x 60=120 s

 $\omega=\omega_{0}+\alpha t$

= $60-\frac{1}{5}\times 120=60-24$

 $\therefore$    $\omega$ =36 rad/s

 As, angular momentum.  L= l $\omega$

 substituting  the values  in the above relation, 

We get  L= 2 x36= 72 kg m2 /s

If the electron in hydrogen atom jumps from second Bohr orbit to ground state and difference between 1energies of the two states is radiated in the form of photons. if the work function of the material is 

[ Energy of electron in nth orbit = $-\frac{13.6}{n^{2}}eV$]

Answer:

Explanation:

 The energy difference between two sates  is given as,

$\triangle E=E_{2}-E_{1}=\frac{-13.6}{2^{2}}-(\frac{-13.6}{1^{2}})$

$\Rightarrow$   $\triangle E=\frac{13.6}{1^{2}}-\frac{13.6}{2^{2}}$

$\Rightarrow$   $\triangle E=13.6\left[\frac{4-1}{4}\right]=13.6 \times\frac{3}{4}$

$\therefore$     $\triangle E$= 10.2 e V

 Since , the energy is radiated  in form of photons, so we have

 Energy of photons =hv =10.2 eV

 From Einstein 's photoelectric equation, we have 

      $hv=\phi_{0}+eV_{s}$

Substituting the given values.

$\therefore$   10.2 eV=4.2e V+e$V_{s}$

$\Rightarrow$     6eV=eV_s

$\therefore$    $V_{s}$= 6 V

A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. after four minutes it becomes 2500 disintegrations per minute.The decay constant per minute is 

Answer:

Explanation:

Given, N₀ = 10,000 disintegration /min

N=2500 disintegeration/min

 t= 4 min

 From the radioactive  decay law , we have

$\frac{N}{N_{0}}=e^{-\lambda t}$

$\therefore$     $\frac{2500}{10000}=e^{-\lambda\times 4}$

 $\Rightarrow$    $ \frac{1}{4}=e^{-4\lambda}\Rightarrow e^{4\lambda}=4$

 $\Rightarrow$    $ 4\lambda=\log_{e}4\Rightarrow 4\lambda=\log_{e}2^{2}$

 $\Rightarrow$   $ 4\lambda=2\log_{e}2$

$\lambda=\frac{2}{4}\log_{e}2$

$\therefore$       $\lambda$= $0.5\log_{e}2$

Two identical light waves having phase difference '$\phi$' propagate in same direction, when they superpose , the intensity of resultant wave is proportional to 

Answer:

Explanation:

For two  coherent sources , the resultant intensity is given as,

$l_{R}=l_{1}+l_{2}+2\sqrt{l_{1}l_{2}}\cos \phi$

 $\therefore$      Fror two identical light waves,

$l_{1}=l_{2}=l$

$\Rightarrow$    $l_{R}=4l\cos^{2}\frac{\phi}{2}$

$\therefore$    $l_{R}\propto\cos^{2}\frac{\phi}{2}$

• Physics - General questions