1
JEE Advanced 2016 Paper 2 Offline
+3
-0
A frame of the reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $$\omega$$ is an example of a non-inertial frame of reference. The relationship between the force $$\overrightarrow F$$rot experienced by a particle of mass m moving on the rotating disc and the force $$\overrightarrow F$$in experienced by the particle in an inertial frame of reference is,

$$\overrightarrow F$$rot = $$\overrightarrow F$$in + 2m ($$\overrightarrow v$$rot $$\times$$ $$\overrightarrow \omega$$) + m ($$\overrightarrow \omega$$ $$\times$$ $$\overrightarrow r$$) $$\times$$ $$\overrightarrow \omega$$,

where, vrot is the velocity of the particle in the rotating frame of reference and r is the position vector of the particle with respect to the centre of the disc. Now, consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the Z-axis along the rotation axis ($$\omega$$ = $$\omega$$ $$\widehat k$$). A small block of mass m is gently placed in the slot at r = (R/2)$$\widehat i$$ at t = 0 and is constrained to move only along the slot.

The distance r of the block at time t is
A
$${R \over 2}\cos 2\omega t$$
B
$${R \over 2}\cos \omega t$$
C
$${R \over 2}({e^{\omega t}} + {e^{ - \omega t}})$$
D
$${R \over 2}({e^{2\omega t}} + {e^{ - 2\omega t}})$$
2
JEE Advanced 2016 Paper 2 Offline
+3
-0
A frame of the reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $$\omega$$ is an example of a non-inertial frame of reference. The relationship between the force $$\overrightarrow F$$rot experienced by a particle of mass m moving on the rotating disc and the force $$\overrightarrow F$$in experienced by the particle in an inertial frame of reference is,

$$\overrightarrow F$$rot = $$\overrightarrow F$$in + 2m ($$\overrightarrow v$$rot $$\times$$ $$\overrightarrow \omega$$) + m ($$\overrightarrow \omega$$ $$\times$$ $$\overrightarrow r$$) $$\times$$ $$\overrightarrow \omega$$,

where, vrot is the velocity of the particle in the rotating frame of reference and r is the position vector of the particle with respect to the centre of the disc. Now, consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the Z-axis along the rotation axis ($$\omega$$ = $$\omega$$ $$\widehat k$$). A small block of mass m is gently placed in the slot at r = (R/2)$$\widehat i$$ at t = 0 and is constrained to move only along the slot.

The net reaction of the disc on the block is
A
$$m{\omega ^2}R\sin \omega t\widehat j - mg\widehat k$$
B
$${1 \over 2}m{\omega ^2}R({e^{\omega t}} - {e^{ - \omega t}})\widehat j + mg\widehat k$$
C
$${1 \over 2}m{\omega ^2}R({e^{2\omega t}} - {e^{ - 2\omega t}})\widehat j + mg\widehat k$$
D
$$- m{\omega ^2}R\cos \omega r\widehat j - mg\widehat k$$
3
JEE Advanced 2016 Paper 1 Offline
+3
-1
A uniform wooden stick of mass 1.6 kg and length $$l$$ rests in an inclined manner on a smooth, vertical wall of height h ( < $$l$$ ) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $$30^\circ$$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio $${h \over l}$$ and the frictional force f at the bottom of the stick are ( g =10 ms-2 )
A
$${h \over l} = {{\sqrt 3 } \over {16}},f = {{16\sqrt 3 } \over 3}N$$
B
$${h \over l} = {3 \over {16}},f = {{16\sqrt 3 } \over 3}N$$
C
$${h \over l} = {{3\sqrt 3 } \over {16}},f = {{8\sqrt 3 } \over 3}N$$
D
$${h \over l} = {{3\sqrt 3 } \over {16}},f = {{16\sqrt 3 } \over 3}N$$
4
IIT-JEE 2012 Paper 2 Offline
+3
-0.75
Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $$\omega$$. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is vr. In one time period (T) of rotation of the discs, vr as a function of time is best represented by A B C D Physics
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