NSEP 2019 24th Nov Question Paper

An observer stands on the platform at the front edge of the first bogie of a stationary train. The train starts moving with uniform acceleration and the first bogie takes 5 seconds to cross the observer. If all the bogies of the train are of equal length and the gap between them is negligible, the time taken by the tenth bogie to cross the observer is

The resistive force on an aeroplane flying in a horizontal plane is given by $$F_f = kv^2$$, where $$k$$ is constant and $$v$$ is the speed of the aeroplane. When the power output from the engine is $$P_0$$, the plane flies at a speed $$v_0$$. If the power output of the engine is doubled the aeroplane will fly at a speed of

A 3.0 cm thick layer of oil (density $$\rho_{oil} = 800\ \text{kg/m}^3$$) floats on water (density $$\rho_w = 1000\ \text{kg/m}^3$$) in a transparent glass beaker. A solid cylinder is observed floating vertically with $$\frac{1}{3}$$ of it in water and $$\frac{1}{3}$$ in the oil. Oil is gently poured into the beaker until the cylinder floats in oil only. The fraction of the solid cylinder in oil now is

A wedge of mass M rests on a horizontal frictionless surface. A block of mass m starts sliding down the rough inclined surface of the wedge to its bottom. During the course of motion, the centre of mass of the block and the wedge system

A uniform circular disc rotating at a fixed angular velocity $$\omega$$ about an axis normal to its plane and passing through its centre has kinetic energy E. If the same disc rotates with an angular velocity $$2\omega$$ about a parallel axis passing through the edge, its kinetic energy will be

In the following figures the velocity-time graphs for three particles 1, 2 and 3 are shown. The magnitude of average acceleration of the three particles, over 10 s, bear the relationship

The potential energy (U) of a particle moving in a potential field varies with its displacement (x) as shown below.

The variation of force F(x) acting on the particle as a function of x can be represented by

A pendulum is made by using a thread of length 300 cm and a small spherical bob of mass 100 g. It is suspended from a point S. The bob is pulled from its position of rest at O to the point A so that the linear amplitude is 25 cm. The angular amplitude in radian and the potential energy of the bob in joule at A are respectively

Consider the following physical expressions. (I) $$\rho v^2$$ where $$\rho$$ is density and $$v$$ is velocity.

(II) $$\frac{Y\Delta L}{L}$$ where $$Y$$ is Young's modulus and $$L$$ is length.

(III) $$\frac{\sigma^2}{\varepsilon_0}$$ where $$\sigma$$ is surface density of charge.

(IV) $$h\rho rg$$ where $$h$$ is the rise of a liquid in a capillary tube of radius $$r$$.

The expressions having same dimensional formula are

Two simple pendulums of lengths 1.44 m and 1.0 m start swinging together in the same phase. The two will be in phase again after a time of

A home aquarium partly filled with water slides down an inclined plane of inclination angle $$\theta$$ with respect to the horizontal. The surface of water in the aquarium

A sound source of constant frequency travels with a constant velocity past an observer. When it crosses the observer the sound frequency sensed by the observer changes from 449 Hz to 422 Hz. If the velocity of sound is 340 m/s, the velocity of the source of sound is

Light of wavelength 640 nm falls on a plane diffraction grating with 12000 lines per inch. In the diffraction pattern on a screen kept at a distance of 12 cm from the grating, the distance of the second order maximum from the central maximum is

If the force acting on a body is inversely proportional to its speed, the kinetic energy of the body varies with time t as

As shown in the figure, a block of mass m is hung from the ceiling by the system of springs consisting of two layers. The force constant of each of the springs is k. The frequency of the vertical oscillations of the block is

Two simple harmonic motions are given by $$x_1 = a\sin\omega t + a\cos\omega t$$ and $$x_2 = a\sin\omega t + \frac{a}{\sqrt{3}}\cos\omega t$$. The ratio of the amplitudes of the first to the second and the phase difference between them respectively are

A particle is projected from the ground with a velocity $$\vec{v} = (3\hat{i} + 10\hat{j})\ \text{ms}^{-1}$$. The maximum height attained and the range of the particle are respectively given by (use $$g = 10\ \text{m/s}^2$$)

A 20 cm long capillary tube stands vertically with lower end just in water. Water rises up to 5 cm. If the entire system is now kept on a freely falling platform, the length of the water column in the capillary tube will be

Position-time graph of a particle moving in a potential field is shown beside. If the mass of the particle is 1 kg its total energy is approximately

Plots of intensity (I) of radiation emitted by a black body versus wavelength $$\lambda$$ at three different temperatures $$T_1$$, $$T_2$$ and $$T_3$$ respectively are shown in figure. Choose the correct statement.

Consider a composite slab consisting of two different materials having equal thickness and equal area of cross-section. The thermal conductivities are K and 2K respectively. The equivalent thermal conductivity of the composite slab is

A large horizontal uniform disc can rotate freely about a rigid vertical axis passing through its centre O. A man stands at rest at the edge of the disc at a point A. The mass of the disc is 22 times the mass of the man. The man starts moving along the edge of the disc. When he reaches A, after completing one rotation relative to the disc, the disc has turned through

Two factories are sounding their sirens at 400 Hz each. A man walks from one factory towards the other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be

The temperature of an isolated black body falls from $$T_1$$ to $$T_2$$ in time t. Then $$t = Cx$$ where x is

Two charges $$-q$$ and $$-q$$ are placed at points $$(0, d)$$ and $$(0, -d)$$. A charge $$+q$$, free to move along X axis, will oscillate with a force proportional to

The average translational kinetic energy of oxygen ($$M = 32$$) molecules at a certain temperature is 0.048 eV. The translational kinetic energy of nitrogen ($$M = 28$$) molecules at the same temperature is (consider the two gases to be ideal)

The log-log graph for a non-linear oscillator is shown below. Assuming the constants to have appropriate dimensions the relationship between time period (T) and the amplitude (A) can be expressed as

In many situations the point source emitting a wave starts moving, through the medium, with velocity V greater than the wave velocity in that medium. In such a case when source velocity (V) is greater than wave velocity (v), the wave front changes

If the average mass of a smoke particle in an Indian kitchen is $$3 \times 10^{-17}$$ kg, the rms speed of the smoke particles at $$27^\circ$$C is approximately

Two wires, made of same material, one thick and the other thin are joined to form one composite wire. The composite wire is subjected to the same tension throughout. A wave travels along the wire and passes the point where the two wires are joined. The quantity which changes at the joint are

The frequency of the third overtone of a closed end organ pipe equals the frequency of the fifth harmonic of an open end organ pipe. Ignoring end correction, the ratio of their lengths $$l_{open} \colon l_{close}$$ is

A concave mirror has a radius of curvature $$R$$ and forms the image of an object placed at a distance $$1.5R$$ from the pole of the mirror. An opaque disc of diameter half the aperture of the mirror is placed with the pole at the centre. As a result

A ray of white light is made incident on the refracting surface of a prism such that after refraction at this surface, the green component falls on the second surface at its critical angle. The colours present in the emergent beam will be

In a compound microscope, having tube-length 30 cm, the power of the objective and the eye-piece are 100 D and 10 D respectively. Then the magnification produced by the microscope when the final image is at the least distance of distinct vision (25 cm) will be

Parallel rays are incident on a glass sphere of diameter 10 cm and having refractive index 1.5. The sphere converges these rays at a certain point. The distance of this point from the centre of the sphere will be

A jet of water from 15 cm diameter nozzle of a fire hose can reach the maximum height of 25 m. The force exerted by the water jet on the hose is

In an electromagnetic wave the phase difference between electric vector and magnetic vector is

A rectangular slab of glass of refractive index 1.5 is immersed in water of refractive index 1.33 such that the top surface of the slab remains parallel to water level. Light from a point source in air is incident on the surface of water at an angle $$\alpha$$ such that the light reflected from the glass slab is plane polarised, the angle $$\alpha$$ is

In a spectrometer the smallest main scale division is $$\frac{1}{3}$$ of a degree. The total number of divisions on the vernier scale attached to the main scale is 60 which coincide with the 59 divisions of the main circular scale. The least count of the spectrometer is

White light is used to illuminate two slits in Young's double slit experiment. Separation between the two slits is b and the screen is at a distance D $$(D \gg b)$$ from the plane of slits. The wavelength missing at a point on the screen directly in front of one of the slits is

In an ink-jet printer, an ink droplet of mass m is given a negative charge q by a computer-controlled charging unit. The charged droplet then enters the region between two deflecting parallel plates of length L separated by distance d (see figure below) with a speed v. All over this region there exists a uniform downward electric field E (in the plane of paper). Neglecting the gravitational force on the droplet, the maximum charge that can be given to this droplet, so that it does not hit any of the plates, is

A converging beam of light is pointing to P. Two observations are made with (i) a convex lens of focal length 20 cm and (ii) a concave lens of focal length 16 cm placed in the path of the convergent beam at a distance 12 cm before the point P. It is observed that

A spherical capacitor is formed by two concentric metallic spherical shells. The capacitor is then charged so that the outer shell carries a positive charge and the inner shell carries an equal but negative charge. Even if the capacitor is not connected to any circuit, the charge will eventually leak away due to a small electrical conductivity of the material between the shells. What is the character of the magnetic field produced by this leakage current?

If a cell of constant emf produces the same amount of heat during the same time in two independent resistors $$R_1$$ and $$R_2$$ when they are separately connected across the terminals of the cell, one after the other. The internal resistance of the cell is

In the circuit shown beside the charge on each capacitor is

A stationary hydrogen atom emits photon corresponding to the first line (highest wave length) of Lyman series. If R is the Rydberg constant and M is the mass of the atom, the recoil velocity of the atom is

Heat is absorbed or evolved when current flows in a conductor having a temperature gradient. This phenomenon is known as

Identify the rank in order from the dimmest to the brightest when all the identical bulbs are connected in the circuit as shown below.

The unit of magnetizing field is

A star undergoes a supernova explosion. Just after the explosion, the material left behind forms a uniform sphere of radius 8000 km with a rotation period of 15 hours. This remaining material eventually collapses into a neutron star of radius 4 km with a period of rotation

A number of identical absorbing plates are arranged in between a source of light and a photo cell. When there is no plate in between, the photo current is maximum. Under the circumstances let us focus on the two statements.
(1) The photo current decreases with the increase in number of absorbing plates.
(2) The stopping potential increases with the increase in number of absorbing plates.

In a nuclear reaction, two photons each of energy 0.51 MeV are produced by electron-positron annihilation. The wavelength associated with each photon is

In the circuit shown if an ideal ammeter is connected between A and B then the direction of current and the current reading would be (assume $$I_s$$ remains unchanged)

Avalanche breakdown in a p-n junction primarily depends on the phenomenon of

A source emits photons of energy 5 eV which are incident on a metallic sphere of work function 3.0 eV. The radius of the sphere is $$r = 8 \times 10^{-3}$$ m. It is observed that after some time emission of photoelectrons from the metallic sphere is stopped. Charge on the sphere when the photoemission stops is

The dc component of current in the output of a half-wave rectifier with peak value $$I_0$$ is

In an experiment on photoelectric effect, the slope of straight line graph between the stopping potential and the frequency of incident radiation gives

According to Bohr's theory the ionization energy of H atom is 13.6 eV. The energy needed to remove an electron from Helium ion $$(He^+)$$ is

The phenomenon inverse to photo electric effect is

A stationary hydrogen atom emits a photon of wavelength 1025 $$A$$. Its angular momentum changes by

A block of mass m = 10 kg is hanging over a frictionless light fixed pulley by an inextensible light rope. Initially the block is held at rest. The other end of the rope is now pulled by a constant force F in the vertically downward direction. The linear momentum of the block is seen to increase by 2 kgm/s in 1 s (in the first second). Therefore,

A ball of mass $$m_1$$ travels horizontally along the x-axis in the positive direction with an initial speed of $$v_0$$. It collides with another ball of mass $$m_2$$ that is originally at rest. After the collision, the ball of mass $$m_1$$ has velocity $$(v_{1x}\hat{i} + v_{1y}\hat{j})$$ and the ball of mass $$m_2$$ has velocity $$(v_{2x}\hat{i} + v_{2y}\hat{j})$$. Identify the correct relationship or relationships

In a real gas

A particle of mass m is thrown vertically up with velocity u. Air exerts an opposing force of a constant magnitude F. The particle returns back to the point of projection with velocity v after attaining maximum height h, then

A pin of small length 'a' is placed along the axis of a concave mirror of focal length f, at the distance u $$(u > f)$$ from its pole. The length of its image is 'b'. If the same object is placed perpendicular to its axis at the same distance u and the length of its image is now 'c', then

A thin rod of length 10 cm is placed along the axis of a concave mirror of focal length 30 cm in such a way that one end of the image coincides with one end of the object. The length of the image may be

The mass of an electron can be expressed as (where c is speed of light in vacuum)

Select the correct statement or statements, out of the following, about diffraction at N parallel slits.

An electric dipole placed in a non-uniform electric field may experience

Two long parallel wires carry currents of equal magnitude (I) but in opposite directions. These wires are suspended from fixed rod PQ by four chords of equal length L as shown. The mass per unit length of each wire is $$\lambda$$, the value of angle $$\theta$$ subtended by two chords OA and OB, assuming it to be small, is