JEE (Advanced) 2008 Paper-2
For the following questions answer them individually
A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $$n_0, \frac{n_0}{2}, \frac{n_0}{6}$$ and $$\frac{n_0}{8}$$, respectively. The angle of incidence $$\theta$$ for which the beam just misses entering Region IV is
STATEMENT-1
For an observer looking out through the window of a fast moving train, the nearby objects appear to movein the opposite direction to the train, while the distant objects appearto be stationary.
and
STATEMENT-2
If the observer and the object are moving at velocities $$\overrightarrow{V_1}$$ and $$\overrightarrow{V_2}$$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $$\overrightarrow{V_2} - \overrightarrow{V_1}$$.
STATEMENT-1
It is easier to pull a heavy object than to pushit on a level ground.
and
STATEMENT-2
The magnitude of frictional force depends on the nature of the two surfaces in contact.
STATEMENT-1
For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT-2
The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by $$\frac{Q}{4 \pi \varepsilon_0 R}$$.
STATEMENT-1
The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
and
STATEMENT-2
Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
The electric field within the nucleus is generally observed to be linearly dependent on r. This implies
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $$\overrightarrow{V_0} = V_0\hat{i}$$. The coefficient of friction is $$\mu$$.
The net external force acting on the disk whenits centre of mass is at displacement x with respect to its equilibrium position is
The centre of mass of the disk undergoes simple harmonic motion with angular frequency $$\omega$$ equal to
