1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
A solid ball of radius R has a charge density $$\rho$$
given by $$\rho$$ = $$\rho$$o (1 $$-$$ $${\raise0.5ex\hbox{\scriptstyle r} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle R}}$$) for 0 $$\le$$ r $$\le$$ R. The electric field outside the ball is :
A
$${{{\rho _o}{R^3}} \over {{ \in _o}{r^2}}}$$
B
$${{{\rho _o}{R^3}} \over {12{ \in _o}{r^2}}}$$
C
$${{4{\rho _o}{R^3}} \over {3{ \in _o}{r^2}}}$$
D
$${{3{\rho _o}{R^3}} \over {4{ \in _o}{r^2}}}$$
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
A man in a car at location Q on a straight highway is moving with speed $$\upsilon$$. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?

A
d
B
$${d \over {\sqrt 2 }}$$
C
$${d \over 2}$$
D
$${d \over {\sqrt 3 }}$$
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
A thin uniform bar of length $$L$$ and mass $$8$$ m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2$$\upsilon$$ and $$\upsilon$$ respectively. The masses stick to the bar after collision at a distance $${L \over 3}$$ and $${L \over 6}$$ respectively from the center of the bar. If the br starts rotating about its center of mass as a result of collision, the angular speed of the bar will be :
A
$${v \over {5L}}$$
B
$${6v \over {5L}}$$
C
$${3v \over {5L}}$$
D
$${v \over {6L}}$$
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle $$\alpha$$ with the horizontal, will be proportional to : (see figure)

A
$$\sqrt {\sin \alpha }$$
B
$${\sin \alpha }$$
C
$$\sqrt {\cos \alpha }$$
D
$${\cos \alpha }$$
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