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 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
$$- m{\omega ^2}R\cos \omega r\widehat j - mg\widehat k$$
2
JEE Advanced 2016 Paper 2 Offline
+3
-0
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V0 and the top plate at $$-$$V0. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

Which one of the following statement is correct?
A
The balls will execute simple harmonic motion between the two plates
B
The balls will bounce back to the bottom plate carrying the same charge they went up with
C
The balls will stick to the top plate and remain there
D
The balls will bounce back to the bottom plate carrying the opposite charge they went up with
3
JEE Advanced 2016 Paper 2 Offline
+3
-0
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V0 and the top plate at $$-$$V0. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

The average current in the steady state registered by the ammeter in the circuit will be
A
proportional to $$V_0^2$$
B
proportional to the potential $${V_0}$$
C
zero
D
proportions to $$V_0^{1/2}$$
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