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 Morning Slot
+4
-1
A force of $$40$$ $$N$$ acts on a point $$B$$ at the end of an $$L$$-shaped object, as shown in the figure. The angle $$\theta$$ that will produce maximum moment of the force about point $$A$$ is given by :

A
$$\tan \theta = {1 \over 2}$$
B
$$\tan \theta = 2$$
C
$$\tan \theta = 4$$
D
$$\tan \theta = {1 \over 4}$$
4
JEE Main 2018 (Online) 15th April Morning Slot
A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod horizontal, a mass $$m$$ is suspended from its end $$A.$$A$$set of$$(m,x)$$values is recorded. The appropriate variables that give a straight line, when plotted, are : A$$m,x$$B$$m,{1 \over x}$$C$$m,{1 \over {{x^2}}}$$D$$m,{x^2}