JEE 2013 :: Advanced 2013 :: Physics 2013

• Advanced 2013 - Physics 2013
• Advanced 2013 - Chemistry 2013
• Advanced 2013 - Mathematics 2013

A solid sphere of radius R and density $\rho$  is attached to one end of a massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3$\rho$. The complete arrangement is placed in a liquid of density 2$\rho$  and is allowed to reach equilibrium. The correct statement(s) is (are)

Answer:

Explanation:

 On small sphere

  $\frac{4}{3}\pi R^{3}(\rho)g+kx=\frac{4}{3}\pi R^{3}(2\rho) g$    ......(i)

  On second sphere (large)

  $\frac{4}{3}\pi R^{3}(3\rho)g=\frac{4}{3}\pi R^{3}(2\rho) g+kx$   .....(ii)

 By Eqs. (i) and (ii) , we get

    x= $\frac{4\pi R^{3}\rho g}{3k}$

A particle of mass M and positive charge Q, moving with a  constant velocity   $u_{1}=4\hat{i}ms^{-1}$, enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x=0 to x=L for all values of y. After passing through this region , the particle emerges on the other side after 10 milliseconds with  a velocity   $u_{2}=2(\sqrt{3}\hat{i}+\hat{j})ms^{-1}$. The correct statement(s) is (are)

Answer:

Explanation:

 u= 4 $\hat{i}$ : v  $=2(\sqrt{3}\hat{i}+\hat{j})$ 

According  to the figure , magnetic field should be in $\otimes$ direction , or along -z direction

 Further ,   $\tan\theta =\frac{v_{y}}{v_{x}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}}$

   $\therefore$     $\theta =30^{0} or\frac{\pi}{6}$

 = angle  of v with x-axis

 = angle rotated by the particle

  =Wt $=\left(\frac{BQ}{M}\right)t$

  $\therefore$      $B=\frac{\pi M}{6Qt}$

                             $=\frac{50\pi M}{Q}$   units   9as t =10^-3  second)

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C, The switch S₁ is pressed first to fully charge the capacitor C₁  and then released. The switch S₂ is then pressed to charge the capacitor C₂, After sometime S₂  is released and then S₃   is pressed, after some time

Answer:

Explanation:

 After  pressing S₁ charge on upper plate of C₁  is +2CV₀

 After pressing S₂ this charge equally distributes in two capacitors. Therefore charge upper plates of both capacitors will be +CV₀

 When S₂ is released  and S₃  is pressed charge on the upper plate of C₁ remains unchanged (=+CV₀ ) but charge on upper plate of C₂ is according to new battery (-CV₀)

A horizontal  stretched string , fixed at two ends, is vibrating in its fifth harmonic according to the equation.   y(x,t')=(0.01m)[sin (62.8 m^-1) x]  cos [(628 s^-1)t].

Assuming $\pi$ =3.14 , the   correct statement (s) is (are)

Answer:

Explanation:

 Number of nodes =6

  From the given equation , we can see that 

        $k=\frac{2\pi}{\lambda}=62.8 m^{-1}$

 $\therefore$      $\lambda=\frac{2\pi}{62.8}m=0.1m$

  $l=\frac{5\lambda}{2}m=0.25m$

 The mid point  of the string is P ,an antinode

$\therefore$  maximum displacement=0.01 m 

   $\omega = 2\pi f=628 s^{-1}$

  $\therefore$     $f=\frac{628}{2\pi}=100 Hz$

 But this si fifth harmonic  freequency .

$\therefore$   Fundamental  frequency f₀

   $=\frac{f}{5}=20 Hz$

Two non conducting solid spheres of radii R and 2R, having uniform volume charge densities  $\rho_{1}$  and $\rho_{2}$ respectively, touch each other. The net electric field at a distance  2R from the centre of the smaller sphere, along the line joining the centre of the spheres, is zero. The ratio   $\frac{\rho_{1}}{\rho_{2}}$ CAN BE

Answer:

Explanation:

At point P

 If resultant electric field is zero then,

$\frac{KQ_{1}}{4R^{2}}=\frac{KQ_{2}}{8R^{3}}R$

 $\frac{\rho_{1}}{\rho_{2}}=4$

  At point Q

If resultant elecric field is zero  then

$\frac{KQ_{1}}{4R^{2}}+\frac{KQ_{2}}{25R^{2}}=0$
$\frac{\rho_{1}}{\rho_{2}}=-\frac{32}{25}(\rho_{1}$ must be negative )

• Advanced 2013 - Physics 2013
• Advanced 2013 - Chemistry 2013
• Advanced 2013 - Mathematics 2013