1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1 A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $$\omega$$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $$\mu$$. The beaker will revolve with the disc if :

A
$$R \le {{\mu g} \over {2{\omega ^2}}}$$
B
$$R \le {{\mu g} \over {{\omega ^2}}}$$
C
$$R \ge {{\mu g} \over {2{\omega ^2}}}$$
D
$$R \ge {{\mu g} \over {{\omega ^2}}}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1 For a particle in uniform circular motion, the acceleration $$\overrightarrow a$$ at any point P(R, $$\theta$$) on the circular path of radius R is (when $$\theta$$ is measured from the positive x-axis and v is uniform speed) :

A
$$- {{{v^2}} \over R}\sin \theta \widehat i + {{{v^2}} \over R}\cos \theta \widehat j$$
B
$$- {{{v^2}} \over R}\cos \theta \widehat i + {{{v^2}} \over R}\sin \theta \widehat j$$
C
$$- {{{v^2}} \over R}\cos \theta \widehat i - {{{v^2}} \over R}\sin \theta \widehat j$$
D
$$- {{{v^2}} \over R}\widehat i + {{{v^2}} \over R}\widehat j$$
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1 A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A
the same throughout the motion.
B
minimum at the highest position of the circular path.
C
minimum at the lowest position of the circular path.
D
minimum when the rope is in the horizontal position.
4
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1 A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

A
B
C
D
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