AIPMT 2015

The positions vector of a particle \(\overrightarrow R\) as a function of time is given by \(\overrightarrow R\) = 4sin(2\(\pi\)t)\(\widehat i\) + 4cos(2\(\pi\)t)\(\widehat j\). Where R is in meters, t is in seconds and \(\widehat i\) a...

A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the ...

A particle is executing a simple harmonic motion. Its maximum acceleration is \(\alpha\) and maximum velocity is \(\beta\). Them, its time period of vibration will be

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same le...

The value of coefficient of volume expansion of glycerin is 5 \(\times\) 10\(-\)4 K\(-\)1. The fractional change in the density of glycerin for a rise of 40oC in its temperature, is

Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then

A force \(\overrightarrow F = \alpha \widehat i + 3\widehat j + 6\widehat k\) is acting at a point \(\overrightarrow r = 2\widehat i - 6\widehat j - 12\widehat k\). The value of \(\alpha\) for which angular momentum about origin is conse...

Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass ...

An automobile moves on a road with a speed of 54 km h\(-\)1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of averag...

The input signal given to a CE amplifier having a voltage gain of 150 is Vi = 2cos(15t + \({\pi \over 3}\)). The corresponding output signal will be

In the given figure, a diode D is connected to an external resistance R = 100 \(\Omega\) and an e.m.f. of 3.5 V. If the barrier potential developed across the diode is 0.5 V, the current in the citcuit will be

If dimensions of critical velocity \(\upsilon\)c of a liquid flowing through a tube are expressed as \(\left[ {{\eta ^x}{\rho ^y}{r^z}} \right]\) where \(\eta ,\rho\) and r are the coefficient of viscosity of liquid, density of liquid and...

Two slits in Young's experiment have widths in the ratio 1 : 25. The ratio of intensity at the maxima and minima in the interference pattern, \({{{I_{max}}} \over {{I_{min}}}}\) is

At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 m s\(-\)1 at an angle of 60o with the source observer line as shown in the figu...

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string i...

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K\(-\)1 mol\(-\)1. If the speed of sound in this gas at NTP is 952 m s\(-\)1, then the heat capacity at constant pressure is
(Ta...

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle \(\theta\) to its initial direction and has...

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is
(Take g = 10 m s...

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 \(\times\) 103 kg/m3 and g = 10 m/s2 then the power (in watt) is

Two particles A and B, move with constant velocities \(\overrightarrow {{v_1}}\) and \(\overrightarrow {{v_2}}\). At the initial moment their position vectors are \(\overrightarrow {{r_1}}\) and \(\overrightarrow {{r_2}}\) respectively....