Basic Physics Questions and Answers

3 107g 4 10 g 52 An assembly of identical spring mass systems is placed on a smooth horizontal surface as shown At this instant the springs are relaxed The left mass is displaced to the left and the right mass is displaced to the right by same distance and released The resulting collision is elastic The time period of the oscillations of system is 1 2 3 2m E m m mm 2 2 4 2m m 2k m

11 There is a current of 40 A in a wire of 10 6 square metre area of cross section If the number of free electrons per cubic metre is 1029 then the drift velocity will be 1 1 25 x 10 m s 2 2 5 x 10 3 m s 3 25 x 10 3 m s 4 25 x 103 m s

55 In damped oscillations damping force is directly proportional to speed of oscillator If amplitude becomes half of its maximum value in 1s then after 2 s amplitude will be Initial amplitude A 2 3 A 4 3A 1 TH sp 1 2 3 4

In the following diagram the charge and potential difference across 8 F capacitance will be nearly 7 F HHK HE HH 6 F 4 F 8 F 9 F 9 F HE 36 F 40 V 1 320 L C 40 V 2 420 C 50 V

The first three moments of a distribution about the value 2 of the variable are 1 16 and 40 Show tha the mean is 3 the variance is 15 andu 86 Also show that the first three moments about x are 3 24 and 76

2 A cheese is being wound on a spindle driven precision winder at constant winding speed The ratio of spindle and traverse rpm is 12 1 The length of traverse is 15 cm The final and initial package diameters are 20 cm and 10 cm respectively If the spindle rpm at the start of winding is 1000 then calculate the spindle rpm at the end if the net winding rate is constant

Calculate the value of the constant N in the given radial function when is normalized The radial function is defined as follows R r Nr e Here N is the normalized constant and a is the positive constant A B 1 3 2 4 2 3 2 r 1 C 2 D q 2 3 2

cm 49 A mass m is attached to two springs of same force constant K as shown in following four arrangements If T T T and T respectively be the time periods of oscillation in the following arrangements in which case time period is maximum a K K m c 1 a wwwwwww K 0000000000 b K 00000 00000 2 b m

B Short Answer Questions Use separate answer sheet for answers Attach with Question page 1 You are given a rectangular block of glass and are asked to identify the type of glass from which it is made Describe a simple experiment involving refraction that could be used to identify the type of glass T I 2

Calculate the surface temperature of the planet if the energy radiated by unit area in unit time is 5 67 x 10 watt Planet may be assumed to black body 1 1273 C 2 1000 C 3 727 C 4 727 K

A body of mass 5 kg is suspended by the strings making angles 60 and 30 with the horizontal 60 a T 25 N c T 25 3 N A a b C c d 5kg T b T 25 N d T 25 3 N B a d D b c

A rocket with a lift off mass 2 x 104 kg is blasted upwards with an intial acceleration of 5 m s 2 The initial thrust of the blast is Take g 10 m s 1 2 105 N 3 4 105 N 2 3 105 N 4 5 105 N

68 Suppose a vertical tunnel is along the diameter sphere of uniform mass density p If a body of mass m is thrown in this earth assumed to be a distance y from the tunnel its acceleration at a centre is given by 4 3 4 c 3 a Goym D 10 to m b d D D 6 3 4 4 3 G

spied cillation 58 The SHM of a particle is given by the equation x 2 sin est 4 cos cof Its amplitude of oscillation is 1 4 units 2 2 units 3 6 units 4 2 5 units 59 If two mutually perpendicular simple harmonic

An increases in pressure required to decreases the 200 litres volume of a liquid by 0 004 in container is Bulk modulus of the liquid 2100 MPa 1 188 kPa 3 18 8 kPa 2 8 4 kPa 4 84 kPa

A block of mass 2 kg is pulled along a smooth horizontal surface by a horizontal force F Find the normal force exerted on the block by the surface What must be the force F if the block is to gain a horizontal velocity of 4 0 m s in 2 0 s starting from rest

O A uniform circular disc of mass M and radius R is having a point mass M at its circumference is performing rolling without slipping over a rough horizontal surface as shown Acceleration of point O is a towards right If N is the normal reaction on disc by the horizontal surface at this instant then M R 1 N 2 Mg 3 N 2Mg Rough TTT 0 a Point mass M 2 N Mg 4 N 2Mg

The Two blocks m 5 kg m 7 kg shown in the figure connected by a heavy uniform rope of mass m 4 kg An upward force of F 200 N is applied as shown Calculate F m m m 4 kg 45 a acceleration of the system b tension at the top of heavy rope c tension at mid point of the rope

14 Consider the following circuits AHME A THHE 1 3 0 02 V A A B C On plugging the key the voltmeter ammeter is likely to be damaged 1 in circuit A 2 in circuit C HHHO D 4 in circuit D A

64 A solid sphere of mass M and radius R has a spherical cavity of radius R 2 such that the centre of cavity is at a distance R 2 from the centre of the sphere A point mass m is placed inside the cavity at a distance R 4 from the centre of sphere The gravitational force on mass m is 14 GMm 11GMm R c R a b GMm 2R d GMm R

A solid sphere moves with linear velocity v to the righ and angular velocity w in anticlockwise direction on rough horizontal surface as shown The sphere does not perform pure rolling and stops after sometime T radius of the sphere is TTTT Rough TT77

3 Hyperbolic 4 Elliptical 3 A hollow metal sphere is filled with water through a small hole in it It is hung by a long thread and is made to oscillate Water slowly flows out of the hole at the bottom Select the correct variation of its time period 1 The period will go on increasing till the sphere is empty 2 The period will go on decreasing till the sphere is empty 3 The period will not be affected at all 4 The period will increase first then decrease to initial value till the sphere is empty ower 8 Pusa Road New Delhi 110005 Ph 011 47623456

Two coils have self inductances L 4 mH and L2 8 mH Current in both the coils is increasing at same rate At an instant when power given to the two coils is same find ratio of currents in the inductors Only one correct answer A 2 B C 13 14

Meter bridge is said to be balanced when 1 Point a galvanometer shows null deflection b current flowing through the galvanometer is zero c the points between which galvanometer is connected are equipotential d all of these

Two cylinders A and B of equal capacity ar connected to each other via a stopcock contains a gas at standard temperature an pressure B is completely evacuated Th entire system is thermally insulated Th stopcock is suddenly opened What is effe on internal energy of gas NCERT Pg 32

magnification of the image formed by one of Find the focal length of the lens and the separation between the two halves Draw the ray diagram for image formation A ray of light travelling in air is incident at grazing angle incident angle 90 on a long rectangular slab of a transparent medium of thickness t 1 0 m The point of incidence is the origin A 0 0 The medium has a variable index of refraction n y given by n y ky 3 2 1 1 2 where k 1 0 meter 3 2 val An image Y is formed of a point object X by a lens whose t 1 0m 1 8m X 1996 AIR P x y B x y MEDIUM A 0 0 AIR The refractive index of air is 1 0 Yay Obtain a relation between the slope of the trajectory of the ray at a point B x y in the medium and the incident angle at that point Obtain an equation for the trajectory y x of the ray in the medium Determine the coordinates x1 y of the point P where the ray intersects the upper surface of the slab air boundary indicate the path of the ray subsequently 1995 X

and D D B B A AND and NOT gates respectively C AND and OR gates respectively E None of these B OR and AND gates respectively D OR and NOT gates respectively

A train moves in north direction with a speed of 54 km h A monkey is running on the roof of the train against its motion with a velocity of 36 km h with respect to train The velocity of monkey as observed by a man standing on the ground is 1 5 m s due north 2 25 m s due south 3 10 m s due south 4 10 m s due north

Three smooth ideal pulleys are connected by a light string A mass m is attached to the pulley P3 Assume the strings between two pulleys and between the pulley and the support to be vertical P P The relation between the magnitudes of acceleration of pulley P ap and that of pulley P3 ap is

An infinitely large thin dielectric sheet of positive charge has area density of charge o If point A is at distance a and point B at distance 3a from this sheet then potential difference between B and A VB V will be C a 280 3 a 80 20a

Example 7 3 A threaded rod with 12 turns per cm and diameter 1 18 cm is mounted horizontally A bar with a threaded hole to match the rod is screwed onto the rod The bar spins at the rate of 216 rpm Determine the velocity of the bar with which it will move the length of 1 50 cm along the rod Also find the time taken by it 216 Sol Given frequency n 216 rpm rps 60 1 Length of one turn cm 12 Number of rotations required to move a distance of 1 5 cm Distance 1 5 N 18 Length of one turn 1 12 Therefore angular displacement 0 2 N 2 Angular velocity of the bar w 2 n 2 x Required time t 36T x 18 36 tra 216 60 7 2 rad s 1 Angular displacement 0 Angular velocity w

Three smooth ideat pulleys are connected by a light string A mass m is attached to the puttey Pa Assume the strings between two pulleys and between the pulley and the support to be vertical The relation between the magnitudes of acceleration of puttey P ap and that of puttey Ps an is O an an 201 an OR 30

The inductors of two LR circuits are placed next to each other as shown in the figure The values of the self inductance of the inductors resistances mutual inductance and applied voltages are specified in the given circuit After both the switches are closed simultaneously the total work done by the batteries against the induced EMF in the inductors by the time the currents reach their steady state values is mJ V 5V R 50 L 10mH mmmmmmm M 5mH llllllll L 20mH R 1092 V 20V

1 45J 2 30 J 3 70J 4 20 J 8 An equilateral triangular frame is made of three thin 38 massless rods Three point masses of mass m each are fixed at vertices of the frame as shown The system is rotated with uniform angular speed o about a fixed axis passing through A and normal to the plane of triangular frame Neglect the effect of gravity The tension in rod connecting mass B and C is 0 1 mort 3 mo t 3 m 2 mo t 4 Zero 1 45 J an 2 30 J 3 70J 4 20 J adv fa fa m di fare courant cenfua feren ald ad reft sie fra de fucidad y free A B C 1 mort 3 mo t m 0 2 m moo 4 Zero

ALLEN Twelve persons are initially at 12 corners of a 29 regular polygon of 12 sides of side a Each person now moves with a uniform speed v in such a manner that 1 is always directed towards 2 2 towards 3 3 towards 4 and so on The time after which they meet is 1 2 3 2a v 2 3 2a v 2 3 4 They will never meet ama ya f v af 1 34 1 44 Y fargef YET are free and f m 2 2 m an 2 2a v 2 3 2a v 2 3 2a 3 24 V 4 m fear a a f

2 There is a sufficiently large inclined plane making an angle a with the horizontal A small block is given a velocity of 64 m s perpendicular to the x axis in the plane of the incline the friction coefficient of which is given by u tar a where a is the inclination of the plane Find the magnitude of final velocity in m s of the block

1 g molecule of V 0 contains 1 10 mole of oxygen atom 2 2 mole of V atom 3 1 mole of O atom 4 2 5 mole of O atom 47 1 10 mole O 2 2 mole V 3 1 mole O 4 2 5 mole O T 18

12 There is a sufficiently large inclined plane making an angle a with the horizontal A small block is given a velocity of 64 m s perpendicular to the x axis in the plane of the incline the friction coefficient of which is given by utan a where a is the inclination of the plane Find the magnitude of final velocity in m s of the block

3 40 Q and 30 Q 4 142 and 30 2 In the Wheatstone bridge shown below in order 3 to balance the bridge we must have 100 3002 1302 R UOL 992 www 1 R 30 R 30 2 R 602 R 150 3 R 1 50 R any finite value 4 R 30 R any finite value ALL PHASE 3 40 12 fir fel 100 3092 1 R 302 R 30 2 R 602 R 150 3 R 1 50 R 4 R 30 R 3002 99 1001CMD E H

n elastic ball thrown with a speed vo from ground level collides with a vertical wall when it is moving at right angles to its initial direction of motion and subsequently strikes the ground after a time ossible time of its motion for the given speed of projection Find angle of projection in degrees 2 3 of the maxi

ALLEN Find out the value of current through 202 4 resistance for the given circuit 1 5 A 2 2 A 3 Zero 4 4 A TION 502 ww 1002 202 www 20V f 20 fari TIOV 1 5 A 2 2 A 3 Zero 4 4 A 562 100 202 20V

In a closed vessel 50 ml of A B completely reacts 48 with 200 ml of C according to the following equation 2A B g 5C g 3C B g CA g The composition of gaseous mixture in the system will be 1 100 ml C 50 ml C B 50 ml CA 2 25 ml C 75 ml C B 25 ml CA 3 75 ml C 75 ml C B 25 ml CA 4 10 ml C 25 ml C B 100 ml CA B 50 fcft C 200 feft Arangure quieren aufufren aan 2A B g 5C g 3C B g CA g 1 1 100 ml C 50 ml C B 50 ml CA 2 25 ml C 75 ml C B 25 ml CA 3 75 ml C 75 ml C B 25 ml CA 4 10 ml C 25 ml C B 100 ml CA

Question No 3 Three identical balls are placed on a smooth horizontal surface as shown in figure Each of them is smooth and has mass m Three balls are touching the horizontal surface and fourth is placed above them Assume tha mg balls on the horizontal surface just touch each other The tension in the thread connecting is k find k

value of forces on the velocity is unknown 17 In a region of space a uniform electric field of strength E a uniform magnetic field of induction B and a uniform gravitational field of strength g coexist in mutually perpendicular directions A charge particle is moving with a uniform velocity in this region Once the particle leaves this region and begins moving into another region where there is only gravitational field of strength g its speed begins to decrease How long after departure from the first region will the velocity of the particle become minimum

a big hollow sphere is charged to a 100 V Electricity will flow from the smaller sphere to the bigger one when a the smaller one is placed inside the bigger one and connected by a wire b bigger one placed by the side of the smaller one and connected by a wire c Both are correct d Both are wrong

A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment P If the distance of C from the dipole is r much larger than the size of dipole then the electric field at Q is proportional to A p and r B p and r2 C p and r D p and r E p and r

A projectile is given an initial velocity of 28 i 2j m s where i is along the ground and j is along the vertical If g 10 m s the equation of its trajectory is 1 y x 5x 2 y 2x 5x 3 4y 2x 5x 4 4y 2x 25x slast Leader Achiever Course ALL PHASE 3 2v 4 V Ni yen vele and we unfires an i 2j m s fear en een feen feen tafe 2 1 y x 5x 2 y 2x 5x 3 4y 2x 5x 4 4y 2x25x g 10 m s

instead the shaft would move with a speed of 1 2 cm s 2 15 cm s 3 6 cm s 4 None of these 5 Two blocks one of mass A 1 kg and another 35 B 2 kg are shown in figure A force of 5 N is applied on A Coefficient of friction between A and B is 0 2 and that between B and horizontal surface is zero Find the time taken for the front face of A to coincide with that of B 4 cm A B 8 cm 8 1 2 2s 2 S 3 5N s 4 0 2 s 16 a 21142 144 det o 1 2 cm s 3 6 cm s af k B 2 kg fun Nant ARAB 0 2 1 2 2s 2 Be front face fe fandel 4 cm A oo Ir 2 15 cm s 4 B and 2011 8 cm 3 5N s 4 0 2 s

Problem 12 29 Determine Vout t in the circuit of Fig P12 29 given th Ps t 3u t V R 42 R 10 and L 2 H Us t R L m 2ix ww R2 Vout Figure P12 29 Circuit for Problems 12 29 and 12 30

If an artificial satellite revolves in circular orbit around the earth with a speed equal to half its escape velocity from the earth Then its height above the surface of earth will be A 3200 km Radius of earth 6400 km B 6400 km D 24000 km C 12800 km