1
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads$$-$$1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads$$-$$1).

A
$${M \over {(M + m)}}$$
B
$${{(M + 2m)} \over {2M}}$$
C
$${{2M} \over {(M + 2m)}}$$
D
$${{2(M + 2m)} \over M}$$
2
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
$$R \ge {{\mu g} \over {{\omega ^2}}}$$
3
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?
A
18.75 kgm2
B
1.905 $$\times$$ 105 kgm2
C
19.05 kgm2
D
1.875 $$\times$$ 105 kgm2
4
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $$\omega$$1 and $$\omega$$2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :
A
$${{{I_1}{I_2}} \over {({I_1} + {I_2})}}{({\omega _1} - {\omega _2})^2}$$
B
$${{{{({I_1} - {I_2})}^2}{\omega _1}{\omega _2}} \over {2({I_1} + {I_2})}}$$
C
$${{{I_1}{I_2}} \over {2({I_1} + {I_2})}}{({\omega _1} - {\omega _2})^2}$$
D
$${{{{({\omega _1} - {\omega _2})}^2}} \over {2({I_1} + {I_2})}}$$
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