IIT JEE Advanced & Mains Physics 2018 : Electricity : Rankfile / expected questions IV

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions / Physicsmynd Elite Series  /  Page  IV 

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28 ] A  spherically symmetrical charge distribution has density
{\rho}_{v}=\begin{cases}\begin{matrix}{\rho }_{{0}},0\leq r\leq R\\ 0,r> R\end{matrix}\end{cases}
Then the energy stored in region r < R is – 

A ]  \frac {4\pi {\rho }_{{0}}^{{3}}{R}^{{5}}}{45{\epsilon }_{{0}}}J

B ]  \frac {2\pi {\rho }_{{0}}^{{2}}{R}^{{5}}}{45{\epsilon }_{{0}}}J

C ]  \frac {\pi {\rho }_{{0}}^{{3}}{R}^{{5}}}{45{\epsilon }_{{0}}}J

D ]  \frac {2\pi {\rho }_{{0}}^{{2}}{R}^{{5}}}{90{\epsilon }_{{0}}}J

 

29 ] Two point charges of equal masses and charges  m and  Q respectively are suspended at a common point by two threads of negligible mass and length l .If at equilibrium, the angle of inclination of each thread to the vertical is \alpha  , then  {Q}^{2} is proportional to –

A ]  {{\sin}^{{2}}{\alpha {\tan{\alpha }}

B ] {{\sin}^{{3}}{\alpha {\tan{\alpha }}

C ] {{\tan}^{{2}}{\alpha {\cos{\alpha }}

D ] {{\tan}^{{3}}{\alpha {\sin{\alpha }}

 

30 ] In the above arrangement , if  \alpha is very small , then \alpha is given by – 

A ] \alpha=3\sqrt{{\frac {{Q}^{{2}}}{32\pi {\epsilon }_{{0}}mg{l}^{{2}}}}}

B ] \alpha=4\sqrt{{\frac {{Q}^{{2}}}{16\pi {\epsilon }_{{0}}mg{l}^{{3}}}}}

C ] \alpha=2\sqrt{{\frac {{Q}^{{2}}}{18\pi {\epsilon }_{{0}}mg{l}^{{3}}}}}

D ] \alpha=3\sqrt{{\frac {{Q}^{{2}}}{16\pi {\epsilon }_{{0}}mg{l}^{{2}}}}} 

 

31 ] Consider two conducting planes kept at a particular angle to each other in the xy axis with the point of contact being at the origin . Obviously . work must be done to bring a point charge to the region of contact between the planes. Then , finding the work done ,using the method of images [in the above case ] is  possible if the angle is [ in degrees] –

A ] 20

B ] 30

C ] 40

D ] 50

 

32 ] The issue with the angle in the above case is due to the fact that there is – 

A ] Difficulty in finding the location of the image charge.

B ] Difficulty in finding the location of the equipotential.

C ] Difficulty in finding the location of the charge at infinity .

D ] A and B 

E ] A , B and C 

 

33 ] A charge q is kept in a pyramid ,on the center of it’s base ,which is square shaped . Then the flux through any face of the pyramid is – 

A  ] zero

B ]  \frac{q}{{\epsilon}_{0}}

C ]  \frac{q}{{8\epsilon}_{0}}

D ]  \frac{2q}{{\epsilon}_{0}}

 

34 ]  A hollow cylinder of resistivity \rho has length L .It’s  inner radius is a and outer radius b  . Then the resistance produced when a  potential difference is generated between the ends of the cylinder is – 

A]  R=\frac {\rho L}{\pi \left({{b}^{{2}}-{a}^{{2}}}\right)}

B ]  R=\frac {\rho L}{\pi \left({{b}^{{4}}-{a}^{{4}}}\right)}

C ]  R=\frac {\rho L}{A}

D ]  R=\frac {\rho L}{2A}

 

35 ] In the above case – 

A ] No current flows through the cylinder . 

B ] Current flows parallel to the axis of the cylinder.

C ] Current flows radially outward from the axis of the cylinder

D ] Current flows perpendicular to the axis of the cylinder

 

36 ] Continuing with question no .34 , what if  the potential difference is applied between the inner and outer surfaces of the cylinder ? [ Choose the right combination ]

a ) Current flows parallel to the axis of the cylinder.

b ) Current flows radially outward from the axis of the cylinder

c ) Resistance remains the same .

d ) Resistance becomes \frac {\rho }{2\pi L}In\left({\frac {b}{a}}\right)

e ) Resistance becomes \frac {\rho }{\pi L}In\left({\frac {a}{b}}\right)

f )  No current flows through the cylinder

Answer : – 

A ]  a , e

B }  b , d 

C ]  d , f 

D ]  c , f 

 

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