AIEEE 2004 (Physics) Mock Test

Which one of the following represents the correct dimensions of the coefficient of viscosity?

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:

A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of the ball in $T/3$ seconds?

If $\vec{A}\times \vec{B}=\vec{B}\times \vec{A}$, then the angle between $\vec{A}$ and $\vec{B}$ is:

A projectile can have the same range $R$ for two angles of projection. If $T_1$ and $T_2$ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to:

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

An automobile travelling with speed of $60\text{km/h}$, can brake to stop within a distance of $20\text{m}$. If the car is going twice as fast, i.e $120\text{km/h}$, the stopping distance will be:

A machine gun fires a bullet of mass $40\text{g}$ with a velocity $1200\text{m/s}$. The man holding it can exert a maximum force of $144\text{N}$ on the gun. How many bullets can he fire per second at the most?

Two masses $m_1=5\text{kg}$ and $m_2=4.8\text{kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? (Take $g=9.8{\text{m/s}}^2$)

A uniform chain of length $2\text{m}$ is kept on a table such that a length of $60\text{cm}$ hangs freely from the edge of the table. The total mass of the chain is $4\text{kg}$. What is the work done in pulling the entire chain on the table?

A block rests on a rough inclined plane making an angle of $30^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10\text{N}$, the mass of the block (in kg) is: (take $g=10{\text{m/s}}^2$)

A force $\vec{F}=(5\hat{i}+3\hat{j}+2\hat{k})\text{N}$ is applied over a particle which displaces it from its origin to the point $\vec{r}=(2\hat{i}-\hat{j})\text{m}$. The work done on the particle in joules is:

A body of mass $m$, accelerates uniformly from rest to $v_1$ in time $t_1$. The instantaneous power delivered to the body as a function of time $t$ is:

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?

A ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant a person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_A$ and $I_B$ such that:

A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is:

The time period of an earth satellite in circular orbit is independent of:

If $g$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is:

Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to:

A wire fixed at the upper end stretches by length $l$ by applying a force $F$. The work done in stretching is:

Spherical balls of radius $R$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v$. The retarding viscous force acting on the spherical ball is:

If two soap bubbles of different radii are connected by a tube:

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $\frac{4}{3}\times 1000{\text{kg/m}}^3$. What relationship between $t$ and $t_0$ is true?

A particle at the end of a spring executes simple harmonic motion with a period $t_1$, while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$, then:

The total energy of a particle executing simple harmonic motion is:

The displacement $y$ of a particle in a medium can be expressed as $y=10^{-6}\sin (100t+20x+\pi /4)\text{m}$, where $t$ is in seconds and $x$ in meter. The speed of the wave is:

A particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency ${\omega }_0$. An external force $F(t)$ proportional to $\cos \omega t$ ($\omega \ne {\omega }_0$) is applied to the oscillator. The displacement of the oscillator will be proportional to:

In forced oscillation of a particle, the amplitude is maximum for a frequency ${\omega }_1$ of the force, while the energy is maximum for a frequency ${\omega }_2$ of the force, then:

One mole of ideal monoatomic gas ($\gamma =5/3$) is mixed with one mole of diatomic gas ($\gamma =7/5$). What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be:

Which of the following statements is correct for any thermodynamic system?

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $(T_1,T_2)$, volume $(V_1,V_2)$ and pressure $(P_1,P_2)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be:

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:

The temperature of two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ respectively, are $T_2$ and $T_1$ ($T_2>T_1$). The rate of heat transfer through the slab in a steady state is $\frac{A(T_2-T_1)K}{x}f$, where $f$ is:

A light ray is incident perpendicular to one face of a $90^{\circ }$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^{\circ }$, we conclude that the refractive index $n$ is:

A plano-convex lens of refractive index $1.5$ and radius of curvature $30\text{cm}$ is silvered at the curved surface. At what distance from this lens should an object be placed in order to have a real image of the same size as the object?

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $n$), is:

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is:

An electromagnetic wave of frequency $\nu =3.0\text{MHz}$ passes from vacuum into a dielectric medium with permittivity $ϵ=4.0{ϵ}_0$. Then:

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges $q$ repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is:

A charged particle $q$ is shot towards another charged particle $Q$ which is fixed. With a speed $v$, it approaches $Q$ up to a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distance of approach would be:

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is:

Alternating current cannot be measured by a D.C. ammeter because:

A $6\text{V}$ battery is connected to a network of resistors. If the equivalent resistance of the network is $1.5\Omega$, the total current supplied by the battery is:

The resistance of the series combination of two resistances is $S$. When they are joined in parallel, the total resistance is $P$. If $S=nP$, then the minimum possible value of $n$ is:

An electric current is passed through a circuit containing two wires of the same material connected in parallel. If the length and radii of the wires are in the ratio of $4/3$ and $2/3$, then the ratio of the currents passing through the wires will be:

In a metre bridge experiment, a null point is obtained at $20\text{cm}$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X<Y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $4X$ against $Y$?

Thermistors are usually made of:

Time taken by a $836\text{W}$ heater to heat one litre of water from $10^{\circ }\text{C}$ to $40^{\circ }\text{C}$ is:

The thermo emf of a thermocouple varies with the temperature $\theta$ of the hot junction as $E=a\theta +b{\theta }^2$ in volts where the ratio $a/b$ is $700^{\circ }\text{C}$. If the cold junction is kept at $0^{\circ }\text{C}$, then the neutral temperature is:

The electrochemical equivalent of a metal is $3.3\times 10^{-7}\text{kg}$ per coulomb. The mass of the metal liberated at the cathode when a $3\text{A}$ current is passed for $2\text{seconds}$ will be:

A current $I$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is:

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B$. It is then bent into a circular loop of $n$ turns. The magnetic field at the centre of the coil will be:

The magnetic field due to a current carrying circular loop of radius $3\text{cm}$ at a point on the axis at a distance of $4\text{cm}$ from the centre is $54\mu \text{T}$. What will be its value at the centre of the loop?

Two long conductors, separated by a distance $d$ carry current $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to $3d$. The new value of the force between them is:

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2\text{s}$. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be:

The materials suitable for making electromagnets should have:

In an LCR series a.c. circuit, the voltage across each of the components, $L,C$ and $R$ is $50\text{V}$. The voltage across the $LC$ combination will be:

A coil having $n$ turns and resistance $4R\Omega$ is connected in a circuit with a resistor $R\Omega$. This combination is moved in time $t$ seconds from a magnetic flux $W_1$ weber to $W_2$ weber. The induced current in the circuit is:

In a uniform magnetic field of induction $B$, a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is:

In a LCR circuit, capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged, the inductance should be changed from $L$ to:

A metal conductor of length $1\text{m}$ rotates vertically about one of its ends at angular velocity $5\text{radians per second}$. If the horizontal component of earth’s magnetic field is $0.2\times 10^{-4}\text{T}$, then the e.m.f. developed between the two ends of the conductor is:

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal vs the frequency of the incident radiation gives a straight line whose slope:

The work function of a substance is $4.0\text{eV}$. Then the longest wavelength of light that can cause photoelectron emission from this substance is approximately:

A charged oil drop is suspended in a uniform field of $3\times 10^4\text{V/m}$ so that it neither falls nor rises. The charge on the drop will be: (Take mass of the drop $=9.9\times 10^{-15}\text{kg}$ and $g=10{\text{m/s}}^2$)

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2:1$. The ratio of their nuclear sizes will be:

The binding energy per nucleon of deuteron (${}_1^2\text{H}$) and helium nucleus (${}_2^4\text{He}$) is $1.1\text{MeV}$ and $7\text{MeV}$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is:

An $\alpha$ -particle of energy $5\text{MeV}$ is scattered through $180^{\circ }$ by a fixed uranium nucleus ($Z=92$). The distance of the closest approach is of the order of:

When an npn transistor is used as an amplifier:

For a transistor amplifier in common emitter configuration having load impedance of $1\text{k}\Omega$ ($h_{fe}=50$ and $h_{oe}=25\times 10^{-6}\text{A/V}$), the current gain is:

A piece of copper and another of germanium are cooled from room temperature to $77\text{K}$. The resistance of:

The manifestation of band structure in solids is due to:

When a p-n junction diode is forward biased: