1
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
$${v \over {6L}}$$
2
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
$${\cos \alpha }$$
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :
A
0.25 cm
B
0.37 cm
C
0.75 cm
D
1.00 cm
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
A capacitor C1 = 1.0 $$\mu$$F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors $${C_2} = 3.0\mu F$$ and C3 = 6.0 $$\mu$$F through switch (2), as shown in the figure. The sum of final charges on C2 and C3 is :
A
40 $$\mu$$C
B
36 $$\mu$$C
C
20 $$\mu$$C
D
54 $$\mu$$C
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