AIPMT-MAINS Physics Questions

The dimensions of (μ₀ε₀)⁻¹/² are :

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by :

A car of mass m is moving on a level circular track of radius R. If μₛ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by :

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P₀. The instantaneous velocity of this car is proportional to :

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2m and its moment of inertia about the axle is 200 kgm². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1ms⁻¹ relative to the ground. Time taken by the man to complete one revolution is:

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:

Three masses are placed on the x-axis: 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is:

If vₑ is escape velocity and v₀ is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by:

Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

A slab of stone of area 0.36 m² and thickness 0.1 m is exposed on the lower surface to steam at 100°C. A block of ice at 0°C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is: (Given latent heat of fusion of ice = 3.36 × 10⁵ J kg⁻¹)

An ideal gas goes from state A to state B via three different processes as indicated in the P⁻V diagram: If Q₁, Q₂, Q₃ indicate the heat a absorbed by the gas along the three processes and ΔU₁, ΔU₂, ΔU₃ indicate the change in internal energy along the three processes respectively, then

The equation of a simple harmonic wave is given by y = 3 sin(π/2 (50t - x)). Where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

A train moving at a speed of 220 ms⁻¹ towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the train is: (speed of sound in air is 330 ms⁻¹)

A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is:

Two metallic spheres of radii 1 cm and 3 cm are given charges of −1×10⁻² C and 5×10⁻² C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

The power dissipated in the circuit shown in the figure is 30 Watts. The value of R is:

Cell having an emf ε and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by:

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an α-particle to describe a circle of same radius in the same field?

A magnetic needle suspended parallel to a magnetic field requires √3 J of work to turn it through 60°. The torque needed to maintain the needle in this position will be:

The instantaneous values of alternating current and voltages in a circuit are given as i = 1/√2 sin(100πt) amper and e = 1/√2 sin(100πt + π/3) Volt. The average power in Watts consumed in the circuit is:

In a coil of resistance 10 Ω, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in Weber is:

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to:

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is:

If the momentum of electron is changed by P, then the de Broglie wavelength associated with it changes by 0.5%. The initial momentum of electron will be:

Two radiations of photons energies 1 eV and 2.5 eV, successively illuminate a photosensitive metallic surface of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons is:

The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:

The half life of a radioactive nucleus is 50 days. The time interval (t₂ - t₁) between the time t₂ when 2/3 of it has decayed and the time t₁ when 1/3 of it had decayed is:

The input resistance of a silicon transistor is 100 Ω. Base current is changed by 40 μA which results in a change in collector current by 2 mA. This transistor is used as a common emitter amplifier with a load resistance of 4 kΩ. The voltage gain of the amplifier is:

To get an output Y = 1 in given circuit which of the following input will be correct:

Equal volumes of two monoatomic gases, A and B, at same temperature and pressure are mixed. The ratio of specific heats \( \left( \frac{C_p}{C_v} \right) \) of the mixture will be:

A galvanometer of resistance, G is shunted by a resistance S Ω. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is

A thermocouple of negligible resistance produces an e.m.f. of 40 μV/°C in the linear range of temperature. A galvanometer of resistance 10 Ω whose sensitivity is 1 μA/div, is employed with the thermocouple. The smallest value of temperature difference that can be detected by the system will be

A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to a mass of 3m moving vertically upward (along the y-axis) with velocity 2v. The final velocity of the combination is

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is

The threshold frequency for a photosensitive metal is 3.3 × 10¹⁴ Hz. If light of frequency 8.2 × 10¹⁴ Hz is incident on this metal, the cut-off voltage for the photoelectric emission is nearly

An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, then the value of n is

The r.m.s. value of potential difference V shown in the figure is

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre, will be

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is

A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is μ = 0.5. The distance that the box will move relative to belt before coming to rest on it, taking g = 10 m/s², is

A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27°C to 927°C. The pressure of the gas in the final state is

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction at the center of the ring is :

A zener diode, having breakdown voltage equal to 15 V is used in a voltage regulator circuit shown in figure. The current through the diode is :

In the following figure, the diodes which are forward biased are

Two radioactive nuclei P and Q in a given sample decay into a stable nucleus R. At time t = 0, number of P species are 4N₀ and that of Q are N₀. Half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal the number of nuclei of R present in the sample would be :

Two radioactive nuclei P and Q in a given sample decay into a stable nucleus R. At time t = 0, number of P species are 4N₀ and that of Q are N₀. Half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal the number of nuclei of R present in the sample would be:

Pure Si at 500 K has equal number of electron (nₑ) and hole (nₕ) concentrations of 1.5 × 10¹⁶ m⁻³. Doping by indium increases nₕ to 4.5 × 10²² m⁻³. The doped semiconductor is of :

A thin prism of angle 15° made of glass of refractive index μ₁ = 1.5 is combined with another prism of glass of refractive index μ₂ = 1.75. The combination of the prisms produces dispersion without deviation. The angle of the second prism should be