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# Tutor profile: Rahul P.

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Rahul P.
All India rank 17 in IIT JAM Physics, All India rank 46 in National eligibility test,
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## Questions

### Subject:Physics (Waves and Optics)

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Question:

What is the distance of the second maxima from the center in a double-slit experiment with slit width $$d$$? The separation between the slit plane and the screen is $$D$$. The light used for the experiment has a wavelength $$\lambda$$.

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Rahul P.

In the double-slit experiment, for maxima, the wave should interfere constructively, and therefore, the path difference between the lights coming out of both slits must be an integer multiple of the wavelength. Let the line joining $$n$$th maximum and the mid-point between the slit make an angle $$\theta$$ with the horizontal. Let also the distance of this maxima from the midpoint of the fringes be $$y_n$$. $( \Delta x=n\lambda\\ dsin\theta\approx dtan\theta=n\lambda\\ d\frac{y_n}{D}=n\lambda\\ y_n=\frac{nD\lambda}{d}$) for the second maximum, substitute $$n=1$$ as the first or the central maximum occurs at $$n=0$$. $( y_n=\frac{D\lambda}{d}$)

### Subject:Physics (Newtonian Mechanics)

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Question:

An object of mass $$m$$ is moving with a velocity $$\vec{u}$$ in positive $$x$$-direction. A constant retarding force $$\vec{F}$$ acts on it. How long will the object travels before it stops?

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Rahul P.

The acceleration due to force $$\vec{F}$$ is towards negative $$x$$-direction and can be evaluated using Newton's second law. $( \vec{F}=m\vec{a}\\ \vec{a}=-\frac{|\vec{F}|}{m}\hat{i}$) When the object comes to the rest, the final velocity $$\vec{v}$$ of the object is 0. Apply third equation of motion for the system. $( \vec{v}^2=\vec{u}^2+2\vec{a}.\vec{s}\\ s=\frac{-u^2}{-\frac{|\vec{F}|}{m}}\\ =\frac{mu^2}{|\vec{F}|}$)

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Question:

A rocket moving to the right with half the speed of light relative to an observer. Another rocket is also moving at the same speed to the left as observed by the same observer. Determine the speed of the second rocket as observed from the first rocket.

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Rahul P.

Let the coordinates of rocket 2 be $$(x,t)$$ in the observer's frame. The coordinates of rocket transform according to the Lorentz transformation to $$(x',t')$$ as: $( x'=\gamma(x-(-v)t) \\ t'=\gamma\left(t-\frac{-v}{c^2}x\right)$) here, $$v$$ is the speed of rocket 2 in observer's frame and $$\gamma$$ is the Lorentz factor for rocket 1 frame with respect to the observer given in terms of the speed of rocket 1 $$u$$ as: $( \gamma=\frac{1}{\sqrt{1-\frac{u^2}{c^2}}}$) taking the partial derivative of the transformation equation, $( dx'=\gamma(dx+vdt) \\ dt'=\gamma\left(dt+\frac{v}{c^2}dx\right)$) Now, the speed of rocket 2 in rocket 1 frame is the rate of change of $$x'$$ with respect to $$dt'$$. $( v_{21}=\frac{dx'}{dt'} \\ =\frac{\gamma(dx+vdt)}{\gamma\left(dt+\frac{v}{c^2}dx\right)}\\ =\frac{\frac{dx}{dt}+v}{1+\frac{v}{c^2}\frac{dx}{dt}}\\ =\frac{u+v}{1+\frac{vu}{c^2}}$)

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