1
JEE Main 2017 (Offline)
+4
-1
A slender uniform rod of mass M and length $$l$$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $$\theta$$ with the vertical is

A
$${{2g} \over {3l}}\cos \theta$$
B
$${{3g} \over {2l}}\sin \theta$$
C
$${{2g} \over {3l}}\sin \theta$$
D
$${{3g} \over {3l}}\sin \theta$$
2
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute(rpm) to ensure proper mixing is close to :

(Take the radius of the drum to be 1.25 m and its axle to be horizontal) :
A
0.4
B
1.3
C
8.0
D
27.0
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
A cubical block of side 30 cm is moving with velocity 2 ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

A
5.0
B
6.7
C
9.4
D
13.3
4
JEE Main 2016 (Offline)
+4
-1
A roller is made by joining together two cones at their vertices $$0$$. It is kept on two rails $$AB$$ and $$CD$$, which are placed asymmetrically (see figure), with its axis perpendicular to $$CD$$ and its center $$O$$ at the center of line joining $$AB$$ and $$CD$$ (see figure). It is given a light push so that it starts rolling with its center $$O$$ moving parallel to $$CD$$ in the direction shown. As it moves, the roller will tend to :
A
go straight
B
turn left and right alternately
C
turn left
D
turn right
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