Basic Physics Questions and Answers

Then find value of 1 13 Figure shows a spherical body floating on liquid surface Line AB represents diameter of sphere Assume liquid and material of body makes a non wetting combination with contact angle 143 at the circumference of sphere passing through AB surface tension 0 05N density of liquid 4 10 kg m Density of sphere Dx 10 kg m radius of sphere 2 mm g 10m s Find D A B

NATIONAL INSTITUTE OF TECHNOLOGY SILCHAR ENGINEERING MECHANICS First Second Semester All Branch COURSE NO ME 101 ASSIGNMENT 25 1 A slender prismatic bar AB is supported in a horizontal position as shown in Fig A At what distance x from the hinge A should the vertical string DE be attached to the bar in order that when it is cut there will be no immediate change in the reaction at 4 Ans x 21 3 2 A homogeneous square plate of weight W and having dimensions a hangs in a vertical plane by two pins A and B as shown in Fig B Calculate and vertical the horizontal components of the reaction at A an instant after the pin at B is removed Ans X 3W 8 Y 5W 8 nive 0 71 FIG C X 3 10 A slender prismatic bar of total length 21 and weight 2W is bent in a right angle at its middle point O and hangs from a hinge at this point as shown in Fig G Find the maximum angular velocity that the bar will acquire if released from rest in the position shown Ans Om 0 621g l W FIG A 11 If the slender prismatic bar AB shown in Fig H is released from rest in the horizontal position and rotates about A under the influence of gravity find the reaction at A as it swings through the vertical positions Ans R 5W 2 C FIG B 7 A horizontal circular disk of uniform thickness radius a and weight W can rotate freely about its vertical geometric axis Fig F Along a circular track of radius r a particle of weight Q is travelling Initially the disk and the particle are rest what angular velocity will the disk acquire if the particle begins to travel along the track with a constant speed v relative to the disk Assume W 10 lb Q 1 lb a 10 in r 6 in v 4 fps Ans u 0 537 sec 3 In Fig C a wood block of weight W 5 lb rests on a horizontal plane and is attached to a fixed hub O by a horizontal string as shown A revolver bullet of weight w 1 oz is fired horizontal into the center of the block in the direction normal to the plane of the figure with velocity v 2 000 fps Calculate the number of revolutions that the block will make around the vertical axis before coming to rest if the coefficient of friction between the block and plane is 1 4 Neglect the dimensions of the block Ans 3 revolutions 777 2 wiffe LTPC 3104 2444 8 Owing to cooling the linear dimensions of a solid homogeneous sphere uniformly rotating about a diameter diminish by 0 1 per cent What effect will this have on the angular velocity of there is no external moment with respect to the diameter of the sphere Ans The angular velocity increases by 0 2 percent B 9 The wheel of a small gyroscope is set spinning by pulling on a string wound around the shaft The moment of inertia of the wheel is 0 045 Ib sec2 in and the diameter of the shaft on which the string is wound is 1 2 in If 36 in of string is pulled off with a constant force of 12 lb what rpm will be imparted to the wheel Ans n 1 324 rpm FIG G FIG F FIG 11 lb at a radius of 1 ft tons Calculate the maximum and minimum force transmitted to the rall when the speed of the locomotive is 60 mph 5 A rotor A initially at rest is suddenly connected to a rotor B having the initial angular velocity by means of a clutch C Fig D What common angular velocity will the two system acquire if the moment of inertia of the system A is la and that of the system B Is Neglect friction in the bearings Ans co la b FIG D 6 A prismatic bar AB of weight W and length 21 carries two balls M and Nof equal weights Wand is rotating with uniform angular velocity con about the vertical Z axis perpendicular to the bar and through its center of gravity Fig E The balls are kept at equal distances from the axis of rotation by f the strings strings What will be the new angular velocity of the system are suddenly cut and owing to centrifugal forces the balls come to the extreme positions P and Q with distances from the axis of rotation equal to The following numerical data are given we 2 sec W 5 lb 212 70 in W 12 lb 21 30 in and 21 45 in Assume in calculation that the mass of the bar is distributed along its axis and the masses of the balls concentrated at their centers Ans 0 520 3 27 sec A S P O 1 FIG E 12 A slender prismatic bar DE of length I and weight W is rigidly attached at its mid point C to a shaft AB and makers therewith an angle a as shown in Fig L Determine the kinetic energy T of the bar of it rotates with constant angular velocity about AB The following numerical data are given W 20 lb 1 40 in a 45 and the uniform angular speed is 200 rpm Ans T 755 in lb 13 A homogeneous slender prismatic bar AB of length and weight Wis hinged at its lower end A and can rotate freely in the vertical plane as shown in Fig J If the bar is released from rest in the unstable position and falls over under the influence of gravity calculate the horizontal component of the reaction at A when 0 30 Ans X 0 225 W AS 4 16 A homogeneous plate 1 ft square is supported in a vertical plane as shown in Fig L a If the pin at B is removed what angular velocity K um will the plate acquire by the time the diagonal AC becomes vertical b Calculate vertical reaction Ra for the instant when the diagonal AC of the square is vertical Ans a co 4 47 rad sec b R 1 44W FIG I lowest position B 2g l 14 What initial angular velocity should be given to the bar AB in Fig J in the top position in order that it will swing through the vertically below A with angular velocity 20 Ans 15 In Fig K a rotor of weight W 386 lb and radius of gyration is 4 in is mounted on a horizontal shaft and set in rotation by a falling weight W 386 lb as shown If the system is released from rest find the velocity of the block after it has fallen through a distance of 10 ft Ans v 11 35 fps FIG J QA W WY PIG K HG L

A part amplitude becomes 1 m the amplitude of oscillation 4 sec before it was 27 if xm represents amplitude at t 0 m 3 3 Xm Xm 27 1 3 E after 6 sec What will be 2 whose 1 F Xm 4 None of these

A smooth ball of mass m moving with a uniform velocity Po strikes a smooth uniform rod AB of equal massm lying on a frictionless horizontal table The ball strikes the rod at one end A perpendicular the rod as shown in the figure The collision is perfectly elastic Some physical quantities pertaining to this situation are given in COLUMN I while their values are given in COLUMN II in a different orde Match the values in COLUMN II and quantities in COLUMN I COLUMN I A Final kinetic energy of ball Initial kinetic energy of ball P 9 Angular momentum of rod about its centre of mass Initial angular momentum of the ball about C the centre of mass of the rod B Impulse delivered to the rod Initial momentum of ball Final ki COLUMN rotation of the d 125

Q 23 Moderate O 1 D O 1 D 4 O 25 D 1 A thin glass refractive index 1 5 lens has optical power of 5 D in air Its optical power in a liquid medium with refractive index 1 6 will be 00 11 O

33 One mole of an ideal diatomic gas goes from a to c along the diagonal path in figure The scale of the vertical axis is set by Pab 5 0 kPa and p 2 0 kPa and the scale of the horizontal axis is set by V4 0 m and V 2 0 m During the transition how much energy is added to the gas as heat CvR 5K 2 Pressure kPa Pab Pe a b Va 2 V Volume m A 1 0 10 J C 5 0 x 10 E 4 0 10 ab AE QtW 7 PV Q PV Q PV bc AE Q W B 2 0 10 J D 7 0 10 pv X 3 x10x 4 RA 2x5x10x bo 2 70 2

Encoders are more commonly called Binary Encoder that takes all its data inputs and then converts them into an encoded output So we can say that a binary Encoder is a multi input logic circuit that converts the logic data at its inputs into equivalent code at its output Generally digital encoders produce outputs of codes depending upon the number of data input lines X input encoder has some input lines and Y output lines with common types that includes particular line configurations When two or more inputs are active simultaneously the process is called A first in first out processing B priority encoding C ripple blanking D first in first out processing or priority encoding

harged plate has charge density of 1 x 105 Cm The initial distance of an electron which is moving towards plate cannot strike the plate if it is having energy of 100 eV is Round the answer to 2 decimal places

9 As shown in the figure a very thin sheet of aluminium is placed in between the plates of the condenser Then the capacity Al strip 1 will increase 2 will decrease 3 remains unchanged AY mou or decrease

Assertion Electric lines of force can never cross each other Reason Electric field at a point always superimposes to give one resultant electric field Assertion The magnetic field strength produced by a current carrying solenoid is independent of its length and cross sectional area Reason The magnetic field strength inside the solenoid is uniform Assertion Free electrons always keep on moving in a conductor even then no magnetic force acts on them in the magnetic field unless a current is passed through it Reason The average velocity of a free electron is zero Assertion To convert a galvanometer into an ammeter a small resistance is

Multiplexing is the generic term used to describe the operation of sending one or more signals over a common transmission line at different times or speeds and the device we use to do just that is called a Multiplexer The multiplexer shortened to MUX or MPX is a combinational logic circuit designed to switch input lines through to a output line by the application of a control signal Multiplexers control multiple input lines called channels to the output Multiplexers or MUX s can be made of MOSFET S or relays or current input How many AND gates are used in 1 8 Demux a 2 b 6 c 8 d 5

An ideal fluid is flowing in a steady state from section A to B through a pipe in a vertical plane as shown Select the incorrect statement E A B 1 Total energy per unit volume is the same at both sections A and B 2 The incoming flow rate at A is equal to the outgoing flow rate at B 3 Loss in kinetic energy of the fluid is equal to gain in potential energy from section A to B 4 The flow of fluid from A to B is laminar flow 146 When the pressure on the surface of water is increased 2 V Ap 3 kp Ac 4 kAp 149 The ter K and D second the sur radiatio 1 3 24 2 2 52 3 8 x 1 4 16 x 150 The are spectral figure a

Q 25 Moderate 4 1 00 17 A telescope of diameter 2 m uses light of wavelength 5000 for viewing stars The minimum angular separation between two stars whose image is just resolved by this telescope is 4 10 rad O 0 25 10 rad O 0 31 10 rad

Q 18 4 1 00 14 One of the refracting surfaces of a prism of angle 30 is silvered A ray of light 3 incident at an angle of 60 retraces its path The refractive index of the material of prism is

him will he be able to see A 30 cm B front of the person looks into the mirror from distance 50 cm How much width height of the wall A person is standing in a room of width 200 cm A plane square mirror of lengin 40 cm C Is 50 cm fixed on a D None lang mirror which is 08

contact 18 A variable condenser is permanently connected to a 100V battery If the capacity is changed from 2 F to 10 F then change in energy is equal to 1 2 x 10 J 2 2 5 x 10 2 J 3 3 5 x 10 2 J

ALLEN The relation F ma cannot be deduced from 4 Newton s second law if 1 force depends on time 2 momentum depends on time 3 acceleration depends on time 4 mass depends on time

The capacitance of an air filled parallel plate capacitor is 10 pF The separation between the plates is doubled and the space between the plates is then filled with wax giving the capacitance a new value of 40 x 10 12 farads The dielectric constant of wax is 1 12 0 2 10 0 3 8 0 4 4 2

A cylinder of radius R lies on a horizontal surface A boy wants to throw a ball over the cylinder with minimum possible speed so that the ball is just able to cross the cylinder 10 R Angle of projection for that minimum speed is 0 then A stemn

8 A sample of germanium is doped to the extent of 1014 donor atoms per cm 3 and 7x10 3 acceptor atoms per cm The resistivity of pure germanium at the temperature of the sample is 60 cm Find the total conduction current density due to an applied electric field of 2 V cm m 1 The electron and hole mobilities are given to be 3800 cm V s and 1800 cm V s respectively Ans 52 3 mA cm 2 S

27 Under the action of a given coulombic force the acceleration of an electron is 2 5 x 1022 m s Then the magnitude of the acceleration of a proton under the action of same force is nearly a 1 6 x 10 9 ms c 1 5 x 10 9 ms 2 b 9 1 x 10 ms2 d 1 6 x 10 ms 28 The acceleration for electron and proton due to electrical force of their mutual attraction when ther

02 03 04 05 07 08 09 10 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 61 57 58 59 60 71 66 67 62 63 76 64 65 68 69 70 72 73 74 75 77 70 70 00 Max Mark s 03 A tiny mirror M is fixed on a piece of cardboard placed on a table The cardboard is illuminated by light from a bulb The position of eye with respect to position of bulb is shown in figure as A B C and D In which position mirror will be visible Bulb Options M A O A O D M Eye Bulb Bulb Eye M M B Eye Eye Bulb

these charges a 3 47 x 10 C c 1 67 x 1020 C b 3 47 x 10 C d 1 67 x 1022 C 15 If an object of mass 1 kg contains 4 x 1020 atoms If one electron is removed from every atom of the solid the charge gained by the solid in I g is a 2 8 C b 6 4 x 10 2 C d 9 2 x 10 C c 3 6 x 10 C

ro at the me force angle is ero 42 An electron initially at rest falls a distance of 1 5 cm in a uniform electric field of magnitude 2 x 10 N C The time taken by the electron to fall this distance is a 1 3 x 10 s c 1 6 x 10 10 s 43 The electric field that can balance a charged particle b 2 1 x 10 12 s d 2 9 x 10 s

5 0 55 70 Mark s 03 Multiple Choice Select 1 out of 4 options for the question below In the given figure find 8 which is formed by the first incident ray with the normal k 80 70 P Options O O O O 80 60 45 70 Clear Response N

ween 25 The ratio of magnitude of electrostatic force and gravitational force for an electron and a proton is a 6 6 x 1039 b 2 4 x 1039 c 6 6 x 1029 d 2 4 x 1029 s and and 26 The electrostatic attracting force on a small sphereof ance 03C due to another

9 10 14 15 19 20 24 25 29 30 3 34 35 38 39 40 43 44 45 48 49 50 53 54 55 7 58 59 60 52 63 64 of 67 68 69 70 65 Multiple Choice Select 1 out of 4 options for the question below A tiny mirror M is fixed on a piece of cardboard placed on a table The cardboard is illuminated by light from a bulb The position of eye with respect to position of bulb is shown in figure as A B C and D In which position mirror will be visible 72 73 74 75 77 78 79 80 Bulb Options OOC A M A D c Eye Bulb Bulb Eye M B Eye Eye O

2950 BOL Boge A straight vertical conductor carries a current At a point 5 cm due north of it the magne induction is found to be 20 T due east The magnetic induction at a point 10 cm east of it will 1 5 T north 2 10 T north 3 5 T south in to ouley 4 10 T south A current of 5 A is flowing through a long straight copper wire The ratio of the magnetic induction

ised If w many zontal rack is le on e of is a fs on t at 1 3 21 The block on the loop the loop as shown in figure 3 1 slides without friction At what height from A it starts so that it presses against the track at B with a net upward force equal to its own weight The radius of loop is R Ans 3 R1 h R Figure 3 122

3 1 becomes four times 2 doubled A current carrying power line carries current from west to east The direction of magnetic 17 1m above is f 1 north to south 2 south to north 3 east to west 4 west to east with its plane in the magnetic meridian of the earth When s

5 50 Multiple Choice Select 1 out of 4 options for the question below A particle is moving in a circular path of radius r The displacement after half a circle would be Options zero Tr 2r 2 r Clear Response N

d 3d 2 d 3d 2 d 30 Consider the charges q q and q placed at the vertices of an equilateral triangle of each side 1 The sum of forces acting on each charge is b a 2ne1 4RE0 2 d zero c 4E0 31 A charge Q is placed at the centre of the line joining point charges q and q as shown in figure The and q is ta

Ten small planes are flying at a speed of 150 km h in total darkness in an air space that is 20 x 20 x 1 5 km in volume You are in one of the planes flying at random within this space with no way of knowing where the other planes are On the average about how long a time will elapse between near collision with your plane Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius 10 m a 125 h b 220 h c 432 h d 225 h

5 30 Isothermal elasticity for a gas having y is 3 3 105 N m If the same gas is undergoing adiabatic change then adiabatic elasticity at that instant is 1 3 x 105 N m 2 5 x 105 N m 3 6 105 N m 4 10 105 N m X

Diameter of the Sun 1 4 x 10 m to the diameter of the Earth 1 2746 x 10 m 5 In a shelf there are 6 notebooks each of thickness 20 mm and 6 sheets of paper each of thickness 0 015 mm What is the total thickness of the shelf Express your answer in standard form Recollections A given rational number when repeatedly multiplied by itself can be expressed in exponential form If the powers are odd the negative integer will give a negative value If the powers are even the negative integer will give a positive value 1 Ifa is any non zero integer then a C

Assertion The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1 5 times the product of its pressure and its volume Reason The molecules of a gas collide with each other and the velocities of the molecules change due to collision a Both assertion and reason are true and reason is the correct explanation of assertion b Both assertion and reason are true but reason is not the correct explanation of assertion c Assertion is true but reason is false d Both assertion and reason are false UMS

3 32 A particle moving along the x axis is subjected to a force given by F F ea 1 where Fo and are constants Determine an expression for the work done by this force as the particle moves from the origin to the point x r 0 PAST Ans F ea a r

The velocity v t of a sprinter on a straight track is shown in the graph below v t 11 5 W 1 3 5 2 Determine the evaluaton of each definite integral So v t dt S710 v t dt S4 v t dt So 0 v t dt 10

4 A body of mass 5 kg starts from the origin with an initial velocity 30 40 ms If a c constant force 61 5 N acts on the body the time in which the y component of the velocity becomes zero is a 5 s c 40 s b 20 s d 80 s

Moderate 4 00 37 Two immiscible liquids of refractive indices 1 5 and are filled in glass jar 4 3 each of length 6 cm A light of source sis at the bottom of the jar the apparent depth of light source will be m

The weight of the block is W it is held by a rope which passes around three fixed rough pins It can move vertically between two smooth walls Find the minimum for the force F such that the block does not slide 45 Given W 200 kN and o 0 35 Do not round off intermediate calculations Answer must be in 3 Decimals and in kN

6 13 The number of electrons that must be removed from an electrically neutral silver dollar to give it a charge of 2 4 C is a 2 5 x 10 9 c 1 5 10 19 em gx ep 1 66 b 1 5 x 1019 d 2 5 x 10 19 14 A coin is made up of Al and weighs 0 75 g It has diagonal measures 17 mm

Let f x y 2x 4y 8 x The domain of c for which the leve curve f x y c is an ellipse is O 4 U 4 O 1 U 1 O 2 U 2 O 3 U 3 O 5 U 5

Moderate How much water should be filled in a container 21 cm in height so that it O appears half filled when viewed from the top of the container given that p 4 3 00 20 8 0 cm 10 5 cm

is a 6x10 8 c 6x 10 9 b 1 6 x 1019 d 1 6 x 1018

In a photoelectric experiment the graph of frequency u of incident light in Hz and stopping potential V in volts is shown below From figure the value of the Planck s constant is e is the elementary charge Question Type Single Correct Type 1 V Volts e ab a v Hz

b c d w and cannot be compared a 3 c 1 4 A Carnot refrigerator extracts heat from water at 0 C 50 A gas e and rejects it to room at 24 4 C The work required by the refrigerator for every 1 kg of water converted into ice is indicate Latent heat of ice 336 kJ kg a 24 4 k denotes c 336 k b 30 kJ d 11 2 kJ

If the radius of earth shrinks to nR n 1 where R is the radius of earth then the time period of rotation of earth about its axis will become A 241 hour C 241 hour B 24 hour n 24 D 2 hour n

The amplitude of a wave disturbance propagating in the positive x direction is given by y 1 1 x at time t 0 and by y 1 1 x 1 at t 2 seconds where x and y are in metres The shape of the wave disturbance does not change during the propagation Find the velocity of the wave

A uniform electric field and a uniform field are acting along the same in a certain region If an electron is projected along the direction of the fields with a certain velocity then magnetic direction OIts velocity will decrease O Its velocity will increase It will turn towards right of direction of motion It will turns towards left of