1
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is $$\mu$$, the torque, applied by the machine on the mop is -
A
$$\mu$$FR/2
B
$$\mu$$FR/3
C
$$\mu$$FR/6
D
$${2 \over 3}$$$$\mu$$FR
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is -
A
$${F \over {2mR}}$$
B
$${2F \over {3mR}}$$
C
$${3F \over {2mR}}$$
D
$${F \over {3mR}}$$
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30o from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s$$-$$1) will be (g = 10 ms$$-$$2)

A
$$\sqrt {{{30} \over 7}}$$
B
$$\sqrt {30}$$
C
$${{\sqrt {20} } \over 3}$$
D
$${{\sqrt {30} } \over 2}$$
4
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is $$\theta$$, thrown :

A
tan$$\theta$$ = $${1 \over {2\sqrt 3 }}$$
B
tan$$\theta$$ = $${1 \over 2}$$
C
tan$$\theta$$ = $${2 \over {\sqrt 3 }}$$
D
tan$$\theta$$ = $${1 \over 3}$$
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