1
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then :
(assume the remaining portion to be spherical).
A
v2 = $$y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$$
B
v2 = $$2y\left[ {{{qQR} \over {4\pi {\varepsilon _0}{{\left( {R + y} \right)}^3}m}} + g} \right]$$
C
v2 = $$2y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$$
D
v2 = $$y\left[ {{{qQ} \over {4\pi {\varepsilon _0}{R^2}ym}} + g} \right]$$
2
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
A particle of charge q and mass m is subjected to an electric field
E = E0 (1 – $$a$$x2) in the x-direction, where $$a$$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :
A
$$a$$
B
$$\sqrt {{2 \over a}}$$
C
$$\sqrt {{3 \over a}}$$
D
$$\sqrt {{1 \over a}}$$
3
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Two charged thin infinite plane sheets of
uniform surface charge density $${\sigma _ + }$$ and $${\sigma _ - }$$,
where |$${\sigma _ + }$$| > |$${\sigma _ - }$$|, intersect at right angle.
Which of the following best represents the
electric field lines for this system :
A
B
C
D
4
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
A two point charges 4q and -q are fixed on the x-axis at x = $$- {d \over 2}$$ and x = $${d \over 2}$$ respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will :
A
increase by $${{3{q^2}} \over {4\pi {\varepsilon _0}d}}$$
B
increase by $${{2{q^2}} \over {3\pi {\varepsilon _0}d}}$$
C
decrease by $${{{q^2}} \over {4\pi {\varepsilon _0}d}}$$
D
decrease by $${{4{q^2}} \over {3\pi {\varepsilon _0}d}}$$
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