1
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)$$ upto $$r=R,$$ and $$\rho \left( r \right) = 0$$ for $$r>R,$$ where $$r$$ is the distance from the erigin. The electric field at a distance $$r\left( {r < R} \right)$$ from the origin is given by
A
$${{{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$$
B
$${{4\pi {\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$$
C
$${{4{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$$
D
$${{{\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$$
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
A thin semi-circular ring of radius $$r$$ has a positive charges $$q$$ distributed uniformly over it. The net field $$\overrightarrow E $$ at the center $$O$$ is AIEEE 2010 Physics - Electrostatics Question 178 English
A
$${q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
B
$$ - {q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
C
$$ - {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
D
$$ {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$$
3
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let $$C$$ be the capacitance of a capacitor discharging through a resistor $$R.$$ Suppose $${t_1}$$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $${t_2}$$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $${t_1}/{t_2}$$ will be
A
$$1$$
B
$${1 \over 2}$$
C
$${1 \over 4}$$
D
$$2$$
4
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Two conductors have the same resistance at $${0^ \circ }C$$ but their temperature coefficients of resistance are $${\alpha _1}$$ and $${\alpha _2}.$$ The respective temperature coefficients of their series and parallel combinations are nearly
A
$${{{\alpha _1} + {\alpha _2}} \over 2},\,{\alpha _1} + {\alpha _2}$$
B
$${\alpha _1} + {\alpha _2},\,{{{\alpha _1} + {\alpha _2}} \over 2}$$
C
$${\alpha _1} + {\alpha _2},\,{{{\alpha _1}{\alpha _2}} \over {{\alpha _1} + {\alpha _2}}}$$
D
$${{{\alpha _1} + {\alpha _2}} \over 2},\,{{{\alpha _1} + {\alpha _2}} \over 2}$$
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