1
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
An inclined plane making an angle of 30$$^\circ$$ with the horizontal is placed in a uniform horizontal electric field $$200{N \over C}$$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

[g = 9.8 m/s2; $$\sin 30^\circ = {1 \over 2}$$; $$\cos 30^\circ = {{\sqrt 3 } \over 2}$$]

A
0.46 s
B
0.92 s
C
1.3 s
D
2.3 s
2
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = $${{\sqrt 3 } \over 2}L$$.

A
$${Q \over {4\pi {\varepsilon _0}{L^2}}}$$
B
$${Q \over {3\pi {\varepsilon _0}{L^2}}}$$
C
$${Q \over {2\sqrt 3 \pi {\varepsilon _0}{L^2}}}$$
D
$${{\sqrt 3 Q} \over {4\pi {\varepsilon _0}{L^2}}}$$
3
JEE Main 2021 (Online) 25th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow E$$ through the shaded area is :

A
$${q \over {24{\varepsilon _0}}}$$
B
$${q \over {48{\varepsilon _0}}}$$
C
$${q \over {4{\varepsilon _0}}}$$
D
$${q \over {8{\varepsilon _0}}}$$
4
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)
A
$${\left( {{{2{q^2}} \over {\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}$$
B
$${\left( {{{{q^2}} \over {2\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}$$
C
$${\left( {{{2\pi {\varepsilon _0}m{d^3}} \over {{q^2}}}} \right)^{{1 \over 2}}}$$
D
$${\left( {{{\pi {\varepsilon _0}m{d^3}} \over {2{q^2}}}} \right)^{{1 \over 2}}}$$
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