NSEP 2017 26th Nov Question Paper

Consider two point masses $$m_1$$ and $$m_2$$ connected by a light rigid rod of length $$r_0$$. The moment of inertia of the system about an axis passing through their centre of mass and perpendicular to the rigid rod is given by

Motion of a particle in a plane is described by the non-orthogonal set of coordinates $$(p, q)$$ with unit vectors $$(\hat{p}, \hat{q})$$ inclined at an angle $$\theta$$ as shown in the diagram. If the mass of the particle is $$m$$, its kinetic energy is given by $$\left(\dot{x} = \frac{dx}{dt}\right)$$

A man is going up in a lift (open at the top) moving with a constant velocity 3 m/s. He throws a ball up at 5 m/sec relative to the lift when the lift is 50 m above the ground. Height of the lift when the ball meets it during its downward journey is $$(g = 10\ \text{m/s}^2)$$

When a body is suspended from a fixed point by a spring, the angular frequency of its vertical oscillations is $$\omega_1$$. When a different spring is used, the angular frequency is $$\omega_2$$. The angular frequency of vertical oscillations when both the springs are used together in series is given by

A small pond of depth 0.5 m deep is exposed to a cold winter with outside temperature of 263 K. Thermal conductivity of ice is $$K = 2.2\ \text{Wm}^{-1}\text{K}^{-1}$$, latent heat $$L = 3.4 \times 10^5\ \text{Jkg}^{-1}$$ and density $$\rho = 0.9 \times 10^3\ \text{kgm}^{-3}$$. Take the temperature of the pond to be 273 K. The time taken for the whole pond to freeze is about

A body of mass 4 kg moves under the action of a force $$\vec{F} = (4\hat{i} + 12t^2\hat{j})$$ N, where $$t$$ is the time in second. The initial velocity of the particle is $$(2\hat{i} + \hat{j} + 2\hat{k})\ \text{ms}^{-1}$$. If the force is applied for 1 s, work done is

A racing car moves along a circular track of radius $$b$$. The car starts from rest and its speed increases at a constant rate $$\alpha$$. Let the angle between the velocity and the acceleration be $$\theta$$ at time $$t$$. Then $$\cos\theta$$ is

A small fish, 4 cm below the surface of a lake, is viewed through a thin converging lens of focal length 30 cm held 2 cm above the water surface. Refractive index of water is 1.33. The image of the fish from the lens is at a distance of

A horizontal ray of light passes through a prism of refractive index 1.5 and apex angle $$4^\circ$$ and then strikes a vertical plane mirror placed to the right of the prism. If after reflection, the ray is to be horizontal, then the mirror must be rotated through an angle

An isolated metallic object is charged in vacuum to a potential $$V_0$$ using a suitable source, its electrostatic energy being $$W_0$$. It is then disconnected from the source and immersed in a large volume of dielectric with dielectric constant $$K$$. The electrostatic energy of the sphere in the dielectric is

Two identical coils each of self-inductance $$L$$, are connected in series and are placed so close to each other that all the flux from one coil links with the other. The total self-inductance of the system is

A coil 2.0 cm in diameter has 300 turns. If the coil carries a current of 10 mA and lies in a magnetic field $$5 \times 10^{-2}$$ T, the maximum torque experienced by the coil is

A particle performs simple harmonic motion at a frequency $$f$$. The frequency at which its kinetic energy varies is

In case of real images formed by a thin convex lens, the linear magnification is (I) directly proportional to the image distance, (II) inversely proportional to the object distance, (III) directly proportional to the distance of image from the nearest principal focus, (IV) inversely proportional to the distance of the object from the nearest principal focus. From these the correct statements are

An infinitely long straight non-magnetic conducting wire of radius $$a$$ carries a dc current $$I$$. The magnetic field $$B$$, at a distance $$r$$ $$(r < a)$$ from axis of the wire is

A quantity $$\alpha$$ is defined as $$\alpha = \frac{e^2}{4\pi\varepsilon_0 c \hbar}$$, where $$e$$ is electric charge, $$\hbar = \frac{h}{2\pi}$$ is the reduced Planck's constant and $$c$$ is the speed of light. The dimensions of $$\alpha$$ are

The earth's magnetic field at a certain point is $$7.0 \times 10^{-5}$$ T. This field is to be balanced by a magnetic field at the centre of a circular current carrying coil of radius 5.0 cm by suitably orienting it. If the coil has 100 turns then the required current is about

The equation correctly represented by the following graph is ($$a$$ and $$b$$ are constants)

Which one of the following devices does not respond to the intensity of light incident on it?

Consider a parallel plate capacitor. When half of the space between the plates is filled with some dielectric material of dielectric constant $$K$$ as shown in Fig. (1) below, the capacitance is $$C_1$$. However, if the same dielectric material fills half the space as shown in Fig. (2), the capacitance is $$C_2$$. Therefore, the ratio $$C_1 \colon C_2$$ is

A point source of light is viewed through a plate of glass of thickness $$t$$ and of refractive index 1.5. The source appears

The fraction of the original number of nuclei of a radioactive atom having a mean life of 10 days, that decays during the $$5^{th}$$ day is

The photoelectric threshold wavelength of tungsten is 230 nm. The energy of electrons ejected from its surface by ultraviolet light of wavelength 180 nm is

A slit of width $$a$$ is illuminated by parallel monochromatic light of wavelength $$\lambda$$. The value of $$a$$ at which the first minimum of the diffraction pattern will form at $$\theta = 30^\circ$$ is

A whistle whose air column is open at both ends has a fundamental frequency 500 Hz. The whistle is dipped in water such that half of it remains out of water. What will be the fundamental frequency now? (speed of sound in air is $$340\ \text{ms}^{-1}$$).

The physical quantity that has unit volt-second is

Consider different orientations of a bar magnet lying in a uniform magnetic field as shown below. The potential energy is maximum in orientation

Two identical charged spheres suspended from a common point by two light strings of length $$l$$, are initially at a distance $$d$$ $$(d \ll l)$$ apart due to their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $$v$$. If $$x$$ denotes the distance between the spheres, then $$v$$ varies as

A network of six identical capacitors, each of capacitance $$C$$ is formed as shown below. The equivalent capacitance between the points A and B is

A cylinder on whose surfaces there is a vertical electric field of varying magnitude as shown. The electric field is uniform on the top surface as well as on the bottom surface. Therefore, this cylinder encloses

Two identical solid blocks A and B are made of two different materials. Block A floats in a liquid with half of its volume submerged. When block B is pasted over A, the combination is found to just float in the liquid. The ratio of the densities of the liquid, material of A and material of B is given by

In an X ray tube the electrons are expected to strike the target with a velocity that is 10% of the velocity of light. The applied voltage should be

When observed from the earth the angular diameter of the sun is 0.5 degree. The diameter of the image of the sun when formed in a concave mirror of focal length 0.5 m will be about

The decimal number that is represented by the binary number $$(100011.101)_2$$ is

The excess pressure inside a soap bubble is equal to 2 mm of kerosene (density $$0.8\ \text{g cm}^{-3}$$). If the diameter of the bubble is 3.0 cm, the surface tension of soap solution is

Let $$V$$ and $$I$$ be the readings of the voltmeter and the ammeter respectively as shown in the figure. Let $$R_V$$ and $$R_A$$ be their corresponding resistances. Therefore,

A man stands at rest in front of a large wall. A sound source of frequency 400 Hz is placed between him and the wall. The source is now moved towards the wall at a speed of 1 m/s. The number of beats heard per second will be (speed of sound in air is 345 m/s)

A hollow sphere of inner radius 9 cm and outer radius 10 cm floats half submerged in a liquid of specific gravity 0.8. The density of the material of the sphere is

Rays from an object immersed in water ($$\mu = 1.33$$) traverse a spherical air bubble of radius $$R$$. If the object is located far away from the bubble, its image as seen by the observer located on the other side of the bubble will be

A 10 ohm resistor is connected to a supply voltage alternating between +4 V and $$-2$$ V as shown in the following graph. The average power dissipated in the resistor per cycle is

In the following arrangement the pulley is assumed to be light and the strings inextensible. The acceleration of the system can be determined by considering conservation of a certain physical quantity. The physical quantity conserved and the acceleration respectively, are

Two cells each of emf $$E$$ and internal resistances $$r_1$$ and $$r_2$$ respectively are connected in series with an external resistance $$R$$. The potential difference between the terminals of the first cell will be zero when $$R$$ is equal to

A student uses a convex lens to determine the width of a slit. For this he fixes the positions of the object and the screen and moves the lens to get a real image on the screen. The images of the slit width are found to be 2.1 cm and 0.48 cm wide respectively when the lens is moved through 15 cm. Therefore, the slit width and the focal length of the lens respectively, are

A particle rests in equilibrium under two forces of repulsion whose centres are at distances of $$a$$ and $$b$$ from the particle. The forces vary as the cube of the distance. The forces per unit mass are $$k$$ and $$k'$$ respectively. If the particle be slightly displaced towards one of them the motion is simple harmonic with the time period equal to

In the following circuit the current is in phase with the applied voltage. Therefore, the current in the circuit and the frequency of the source voltage respectively, are

In an atom an electron excites to the fourth orbit. When it jumps back to the lower energy levels a spectrum is formed. Total number of spectral lines in this spectrum would be

The following figure shows the section ABC of an equilateral triangular prism. A ray of light enters the prism along LM and emerges along QD. If the refractive index of the material of the prism is 1.6, angle LMN is

A ball of mass $$m$$ hits directly another ball of mass $$M$$ at rest and is brought to rest by the impact. One third of the kinetic energy of the ball is lost due to the collision. The coefficient of restitution is

An object 1 cm long lies along the principal axis of a convex lens of focal length 15 cm, the centre of the object being at a distance of 20 cm from the lens. Therefore, the size of the image is

Acidified water from certain reservoir kept at a potential $$V$$ falls in the form of small droplets each of radius $$r$$ through a hole into a hollow conducting sphere of radius $$a$$. The sphere is insulated and is initially at zero potential. If the drops continue to fall until the sphere is half full, the potential acquired by the sphere is

The figure of merit of the galvanometer in microampere per division is

The resistance of the galvanometer in ohm is,The series combination of the galvanometer with a resistance of R is connected across an ideal voltage supply of 12V and this time the galvanometer shows full scale deflection of 30 divisions.

 The value of R is nearly

A $$24\ \Omega$$ resistance is connected to a 5 V battery with internal resistance of $$1\ \Omega$$. A $$25\ \text{k}\Omega$$ resistance is connected in series with the galvanometer and this combination is used to measure the voltage across the $$24\ \Omega$$ resistance. The number of divisions shown in the galvanometer is

Now a $$1000\ \mu\text{F}$$ capacitor is charged using the 12 V supply and is discharged through the galvanometer-resistance combination used in the previous question. The current $$i$$ (in ampere) at different time $$t$$ (in second) are recorded. A graph of $$\ln i$$ against $$t$$ is plotted. The slope of the graph is

If Newton's inverse square law of gravitation had some dependence on radial distance other than $$r^{-2}$$, which one of Kepler's three laws of planetary motion would remain unchanged?

A neutral metal bar moves at a constant velocity $$v$$ to the right through a region of uniform magnetic field directed out of the page, as shown. Therefore,

Two moles of hydrogen are mixed with $$n$$ moles of helium. The root mean square speed of gas molecules in the mixture is $$\sqrt{2}$$ times the speed of sound in the mixture. Then $$n$$ is

In the figure shown below masses of blocks A and B are 3 kg and 6 kg respectively. The force constants of springs $$S_1$$ and $$S_2$$ are 160 N/m and 40 N/m respectively. Length of the light string connecting the blocks is 8 m. The system is released from rest with the springs at their natural lengths. The maximum elongation of spring $$S_1$$ will be

Two particles A and B of equal masses have velocities $$\vec{v_A} = 2\hat{i} + \hat{j}$$ and $$\vec{v_B} = -\hat{i} + 2\hat{j}$$. The particles move with accelerations $$\vec{a_A} = -4\hat{i} - \hat{j}$$ and $$\vec{a_B} = -2\hat{i} + 3\hat{j}$$ respectively. The centre of mass of the two particles moves along

A ray is incident on a refracting surface of RI $$\mu$$ at an angle of incidence $$i$$ and the corresponding angle of refraction is $$r$$. The deviation of the ray after refraction is given by $$\delta = i - r$$. Then, one may conclude that

In a series R-C circuit the supply voltage $$V_S$$ is kept constant at 2 V and the frequency $$f$$ of the sinusoidal voltage is varied from 500 Hz to 2000 Hz. The voltage across the resistance $$R = 1000$$ ohm is measured each time as $$V_R$$. For the determination of the $$C$$ a student wants to draw a linear graph and try to get $$C$$ from the slope. Then she may draw a graph of

Two balls A and B moving in the same direction collide. The mass of B is $$p$$ times that of A. Before the collision the velocity of A was $$q$$ times that of B. After the collision A comes to rest. If $$e$$ be the coefficient of restitution then which of the following conclusion or conclusions is or are correct?

A convex lens and a concave lens are kept in contact and the combination is used for the formation of image of a body by keeping it at different places on the principal axis. The image formed by this combination of lenses can be

In a bipolar junction transistor

A particle starting from rest at the highest point slides down the outside of a smooth vertical circular track of radius 0.3 m. When it leaves the track its vertical fall is $$h$$ and the linear velocity is $$v$$. The angle made by the radius at that position of the particle with the vertical is $$\theta$$. Now consider the following observations. $$(g = 10\ \text{m/s}^2)$$ (I) $$h = 0.1$$ m and $$\cos\theta = \frac{2}{3}$$. (II) $$h = 0.2$$ m and $$\cos\theta = \frac{1}{3}$$. (III) $$v = \sqrt{2}\ \text{ms}^{-1}$$. (IV) After leaving the circular track the particle will describe a parabolic path. Therefore,

A small bar magnet is suspended by a thread. A torque is applied and the magnet is found to execute angular oscillations. The time period of oscillations

Two identical rods made of two different metals A and B with thermal conductivities $$K_A$$ and $$K_B$$ respectively are joined end to end. The free end of A is kept at a temperature $$T_1$$ while the free end of B is kept at a temperature $$T_2$$ $$( < T_1)$$. Therefore, in the steady state

If a system is made to undergo a change from an initial state to a final state by adiabatic process only, then

A body of mass 1.0 kg moves in X-Y plane under the influence of a conservative force. Its potential energy is given by $$U = 2x + 3y$$ where $$(x, y)$$ denote the coordinates of the body. The body is at rest at $$(2, -4)$$ initially. All the quantities have SI units. Therefore, the body