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QUESTION: 1

In a series LCR circuit, resistance R = 10 Ω and the impedance *Z* = 20 Ω . The phase difference between the current and the voltage is

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QUESTION: 2

A system consists of two identical particles one particle is at rest and the other particle has an acceleration 'a'. The centre of mass of the system has an acceleration of

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QUESTION: 3

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QUESTION: 4

A small solid cylinder rolls up along a curved surface (fig.) with an initial velocity v. It will ascend up to a height ‘h’ equal to

Solution:

Since the cylinder is rolling, it has translational and rotational kinetic energies. The total kinetic energy is

*K* = (½) *Mv*^{2 }+ (½) *Iω*^{2}

where *M* is the mass, *I* is the moment of inertia and *ω* is the angular velocity of the cylinder. At the highest point, the kinetic energy will be zero since the entire energy will be converted into gravitational potential energy *Mgh* where *h* is the height. So. we have

(½) *Mv*^{2 }+ (½) *Iω*^{2} = *Mgh*

The moment of inertia of the cylinder about its own axis is *I = *(½) *MR*^{2} where *R *is the radius of the cylinder. The angular velocity *ω* = *v/R*. Substituting these in the above equation,

(½) *Mv*^{2 }+ (½)×(½) *MR*^{2} ×*v*^{2}/*R*^{2} = *Mgh*

Or, (¾)*Mv*^{2} = *Mgh*, from which *h* = **3***v ^{2}*/4

QUESTION: 5

A bullet of mass *m* is fired into a block of wood of mass M which hangs on the end of a pendulum and gets embedded in it. When the bullet strikes the wooden block, the pendulum starts to swing with a maximum rise R. The velocity of the bullet is given by

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QUESTION: 6

The electrical resistance of a mercury column in a cylindrical container is *R*. When the same mercury is poured into another cylindrical container twice the radius of cross-section, the resistance of mercury column now is

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QUESTION: 7

Copper and sillicon is cooled from 300 K to 60 K, the specific resistance

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QUESTION: 8

Which of the following statements is correct

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QUESTION: 9

A transformer is used to light a 100*W* and 110*V* lamp from a 220*V* mains. If the main current is 0.5*A*, the efficiency of the transformer is approximately

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QUESTION: 10

An electric dipole consists of two opposite charges of magnitude ± q seperated by 2a. When the dipole is placed in uniform electric field E, to have minimum potential energy, then dipole moment p makes which the following angle with E

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QUESTION: 11

The phase difference between the current and voltage at resonance is

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QUESTION: 12

Five equal capacitors connected in series have a resultant capacitance of 4 $\mu $F. The total energy stored in these, when these are connected in parallel and charged to 400V is

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QUESTION: 13

A body of mass 2 kg is kept by pressing to a vertical wall by a force of 100 N. The friction between wall and body is 0.3. The the frictional force is equal to

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QUESTION: 14

The acceleration due to gravity at a height 1/10th of the radius of the earth above the earth's surface is 8.2 m-s⁻^{2}. Its value at a point at the same distance below the surface of the earth is

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QUESTION: 15

A geostationary satellite

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QUESTION: 16

The maximum wavelength of radiations emitted at 900 K is 4μm. What will be the maximum wavelength of radiations emitted at 1200 K

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QUESTION: 17

The pressure and temperature of two different gases is P and T having the volume V for each. They are mixed keeping the same volume and temperature, the pressure of the mixture will be

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QUESTION: 18

A galvanometer having a resistance of 50 Ω gives a full scale deflection for a current of 0.05A. The length in meter of a resistance wire of area of cross section 2.97 x 10^{ − 3} c m 2 that can be used to convert the galvanometer into an ammeter which can be read a maximum of 5A current is [specific resistance of the wire = 5 x 10^{−7} c m 2 Ω − m ]

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QUESTION: 19

A galvanometer having a resistance of 8 Ω is shunted by a wire of resistance 2 Ω. If the total current is 1 A, then current passing through the shunt will be

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QUESTION: 20

A bar magnet of magnetic moment M is kept in a uniform magnetic field of strength B, making angle θ with its direction. The torque acting on it is

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QUESTION: 21

In old age, arteries carrying blood in the human body become norrow, resulting in an increase in the blood pressure. This follows from

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QUESTION: 22

The moment of inertia of a uniform thin rod of length L and mass M about an axis passing through a point at a distance of L/3 from one of its ends and perpendicular to the rod is

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QUESTION: 23

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity ν₀. the distance travelled by the particle in time t will be

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QUESTION: 24

Which of the following affets the elasticity of a substance?

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QUESTION: 25

A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

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QUESTION: 26

A stone of mass 1 kg tied of the end of a 1 m long string, is whirled in a horizontal circle, with a uniform angular velocity of 2 rad-s⁻^{1}. Tension of the string is

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QUESTION: 27

A parachutist of weight 'w' strikes the ground with his legs fixed and comes to rest with an upward acceleration of magnitude 3 g. Force exerted on him by ground during landing is

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QUESTION: 28

Two white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? (Take wavelength of light =500 nm)

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QUESTION: 29

Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will be

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QUESTION: 30

Range of a projectile is R, when the angle of projection is 30^{o}. Then, the value of the other angle of projection for the same range is

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QUESTION: 31

A plano convex lens is made of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is

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QUESTION: 32

If I, α and τ are the moment of inertia, angular acceleration and torque respectively of a body rotating about any axis with angular velocity ω, then

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QUESTION: 33

The dimensional formula for angular velocity in

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QUESTION: 34

Two forces each of magnitude F, acting o a particle yield a resultant force of magnitude F. The angle between the forces is

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QUESTION: 35

Mercury does not wet glass, wood or iron because

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QUESTION: 36

Two wire with resistances R and 2R are connected in parallel, the ratio of heat generated in 2R and R is

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QUESTION: 37

If R₁ and R₂ are respectively the filament resistances of a 200 watt bulb and 100 watt bulb designed to operate on the same voltage, then

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QUESTION: 38

540 g of ice at 0^{o}C is mixed with 540 g of water at 80^{o}C. The final temp. of the mixture in ^{o}C will be

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QUESTION: 39

If the heat of 110 J is added to a gaseous system, change in internal energy is 40 J. Then the amount of external work done is

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QUESTION: 40

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation v=at + b/t+c; the dimensions of a, b and c are

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QUESTION: 41

Length can not be measured by

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QUESTION: 42

In Young's double slit experiment, the width of the fringes obtained with light of wavelength 6000 Angstrom is 2.0mm. The fringe width, if the entire apparatus is immersed in a liquid of refractive index 1.33, will be

Solution:

Fringe width in Young's double slit experiment β = Dλ /d

When apparatus is immersed in liquid, only wavelength of light (λ) changes

Wavelength of light is liquid,

λ' = λ /n , where n = refractive index of medium

Initial fringe width, β = Dλ /d .....(i)

Fringe width in liquid, β' = Dλ' /d .....(ii)

Dividing Equation (ii) by Equation (i), we get

QUESTION: 43

If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved, then its fundamental frequency will become

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QUESTION: 44

The potential energy of a weight less spring compressed by a distance a is propotional to

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QUESTION: 45

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy . The initial velocity of the shell is :

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