JEE 2014 :: Advanced 2014 :: Physics 2014

• Advanced 2014 - Physics 2014
• Advanced 2014 - Chemistry 2014
• Advanced 2014 - Mathematics 2014

A horizontal circular platform of radius 0.5m  and mass 0.45kg is free to rotate about its axis. Two, assless spring toy-guns, each carrying a steel ball of mass 0.05kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure) . Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have a horizontal speed of  9 ms^-1 with respect to the ground. The rotational speed of the   platform in rad s^-1  after the balls leave  the platform is 

Answer:

Explanation:

Applying conservation of angular momentum.

$2mvr-\frac{MR^{2}}{2}\omega=0$

$\omega=\frac{4mvr}{MR^{2}}$

 Substituting the values , we get

$\omega=\frac{(4)(5\times 10^{-2})(9)(\frac{1}{4})}{45\times10^{-2}\times\frac{1}{4}}=4 rad/s$

A rocket is moving in a gravity-free space with a constant acceleration of 2 ms^-2 along +x direction (see figure). The length of a chamber inside the rocket is 4m. A  ball is thrown from the left and end of the chamber in+x direction with a speed of 0.3 ms^-1 relatives to the rocket. At the same time, another ball is thrown in  -x direction with a speed of 0.2 ms^-1 from its right and relative to the rocket. The time in seconds when the two balls hit each other is 

Answer:

Explanation:

Motion of ball A relative to rocket.

 Consider motion of two balls with respect to rocket.

 Maximum distance of ball A from left wall

    $\frac{u^{2}}{2a}=\frac{0.3\times0.3}{2\times2}$

  = $\frac{0.09}{4}=0.02m$      (as   $0=u^{2}-2as)$

 So, collision of two balls will take place very near to left wall

 Motion of ball B relative to  rocket

  For B      $S=ut+\frac{1}{2}at^{2}$

  $-4=-0.2t-(\frac{1}{2})2t^{2}$

   Solving this equation, we get,

  t= 1.9 s

Nearest integer =2s

Consider an elliptically shaped rail PQ in the vertical plane with OP= 3m  and  OQ=4m. A block of mass 1kg is pulled along the rail from P to Q with a force of  18N. Which is always parallel to line PQ (see figure). Assuming no frictional losses, the kinetic energy of the block, when it reaches Q, is (n x10) j. The value of n is  (take acceleration due to gravity =10 ms^-2 )

Answer:

Explanation:

 From work-energy theorm

 Work done by all forces= change in  kinetic energy

 or    W_F  +W_mg=K_f-K_i

$18\times5+(1\times10)(-4)=K_{f}$

$K_{f}=50J=5\times10 J$

 A galvanometer gives full-scale deflection with 0.006 A current. By connecting it to a 4990Ω resistance, it can be converted into a voltmeter of range 0-30V. If connected to a  $\frac{2n}{249}$ Ω resistance, it becomes an ammeter of range 0-1.5 A. The value of n is 

Answer:

Explanation:

$i_{g}(G+4990)=V$

$\Rightarrow$     $ \frac{6}{1000}(G+4990)=30$

$\Rightarrow$    $G+4990=\frac{30000}{6}=5000$

$\Rightarrow$             G=10Ω

                       V_ab  =V_cd

$\Rightarrow$               $i_{g}G=(1.5-i_{g})S$

 $\Rightarrow$      $ \frac{6}{1000}\times10 = \left( 1.5-\frac{6}{1000}\right)S$

    $\Rightarrow $    $S=\frac{60}{1494}=\frac{2n}{249}$

$\Rightarrow$      $ n=\frac{249\times30}{1494}=\frac{2490}{498}=5$

To find the distance d over which a signal can be seen clearly in foggy conditions, a  railways engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to  S^1/n. The  value of n is 

Answer:

Explanation:

Let    $d=k(\rho)^{a}(S)^{b}(f)^{c}$

 where, k is a dimensionless, then

$[L]=\left[ \frac{M}{L^{3}}\right]^{a}\left[\frac{ML^{2}T^{-2}}{L^{2}T}\right]^{b}\left[\frac{1}{T}\right]^{c}$

 Equating  the powers of M and L , we have

       0=a+b      ........(i)

           1= -3a...........(ii)

Solving these two equations , we get

    $b=\frac{1}{3}$                $\therefore n=3$

• Advanced 2014 - Physics 2014
• Advanced 2014 - Chemistry 2014
• Advanced 2014 - Mathematics 2014