Basic Physics Questions and Answers

5 A smooth uniform solid sphere rolling without slipping with velocity vo collides elastically and head on with a stationary identical sphere placed on a rough horizontal surface The velocity of second sphere when it starts pure rolling is 1 2V0 5 F Vo Rough 2 5V0 7

A bird moves from point 1 2 to 4 2 If the speed of the bird is 20 m s then the velocity vector of the bird is A 5 2 B 61 8j C 0 6i 0 8j D 121 16

Which of the following statement s is are correct A Two unit vectors can add to give a unit vector B A unit vector if rotated through an angle will not be a unit vector As angle between two vectors is increased from 90 to 135 magnitude of their C resultant increases D j k can be said to be components of vector i j k k

A constant horizontal force is applied on the hanging bob of a simple pendulum of mass m starting from vertical position as shown m F The string deflects through a maximum angle 0 F mg 1 tan 0 Find 3 cot 0 10 2 cot 0 4 tan

with the water splashing out parallel to plate Find the force that the plate experiences 5 A laminar stream is flowing vertically down from a tap of cross section area I cm At a distance 10cm below the tap the cross section area of the stream has reduced to 1 2 cm Find the volumetric flow rate of water from the tap 6 Calculate the rate of flow of glycerine of density 1 25 x 10 kg m through the conical section of a

Two isotopes P and Q of atomic weight 10 and 20 respectively are mixed in equal amount by weight After 20 days their weight ratio is found to be 1 4 Isotope P has a half life of 10 days The half life of isotope Q is

Particle X and particle Y are initially positioned at a 0 and 0 b respectively At t 0 the particles X and Y start moving with ui and vj respectively Maximum angular speed of the line joining the particles is 1 3 v U va ub v 4 vb ua 2 4 v u va ubl v U vb ual

At a distance of 23 feet from the base of a flag pole the angle of elevation to the top of a flag that is 3 1 feet tall is 53 2 The angle of elevation to the bottom of the flag is 50 3 The pole extends 1 foot above the flag Find the height of the pole A 28 9 ft B 27 9 ft C 318 ft D 30 8 ft

Two vectors P Q are arranged in such a way that they form adjacent sides of a parallelogram as shown in figure Which of the following options have incorrect relationship A Q P S C R P S P te S R B R P Q D S Q P

Consider a uniformly charged metallic spherical shell of radius R and charge Qas shown in fig The columbic force experienced by the upper half of the metallic spherical shell is Q X R Then value of x is Sr Super60 All R Space for rough work Page 6

A pin welded at the circumference of the wheel forces a T shaped body to move up and down The pin slides freely inside the slot of the yoke as the wheel rotates The 7 shaped body is constrained to move vertically by a set of walls A M yoke Pin Wall a Find the time period of oscillatory motion of point A at the base of the T shaped body

A conducting loop moves with constant velocity 2m s in nonuniform and variable magnetic field B t x T where x is in meter and t is in second s shown in figure The magnitude of emf induced at t 1s is a 1m 1 0 V 2 m s

If two vectors P and 6 are inclined at angle 0 then A Angle between P and is 27 0 B Angle between P and and Q is 0 C Angle between P and 1 is 0 D Angle between P and is 0

A cubical block of mass m 1 kg is placed on a smooth horizontal surface as shown Its centre is tied to a massless and inextensible string of length 10 m and other end of the string is connected to ball of same mass Ball is released from the position shown It falls under gravity and then string becomes taut The kinetic energy of block and ball just after string is taut are KE and KE respectively then g 9 8 m s 1 30

A liquid of density p is filled in a U tube whose one end is open at the other end a bulb is fitted whose pressure is P Now this tube is moved horizontally with acceleration a as shown in the figure During motion it is found that liquid in both column is at same level at equilibrium If atmospheric pressure is P then find the value of P

An astronomical telescope has an objective lens of focal length 100 cm and for relax eye adjustment magnification is 10 The separation between objective and eye piece lens is O O 110 cm 90 cm 10 cm O125 cm

D A rod of length 2 4 m and radius 4 6 mm carries a negative charge of 4 2 x 10 C spread uniformly over it surface The electric field near the mid point of the rod at a point on its surface is a 8 6 x 10 NC c 67 x 10 NC 1 b 8 6 x 10 NC 16210 NG

Consider the situation shown in the figure The switch S is open for a long time and then closed and again steady state reached then 2C X HH Charge flowing from X to Y is Charge flowing from Y to X is Work done by battery is Work done by battery is CV 3 2CV 3 2CV 3 CV 3 2C S H C

Be A uniform metre rule of mass 100 g is balanced on a fulcrum at mark 40 cm by suspending an unknown mass m at the mark 20 cm i Find the value of m ii To which side the rule will tilt if the mass m is moved to the mark 10 cm iii What is the resultant moment now iv How can it be balanced by another mass of 02

entre in in to the hits the small akw 87 The total flux through the faces of the cube with side of length a if a charge g is placed at corner A of the cube is 9 a 11

le d negative z direction is a 10 N b 10 N c 10 N d 10 75 In the question number 74 torque experienced by the system is d 10 a 10 N b 10 N c zero CONTINUOUS CHARGE DISTRU ent b equal to

particles having charges of magnitude q each and alternatively positive and negative are placed at the four corners of the square Select the correct 1 alternative s neglect gravitational effects k Centre of dipole coincidence with the intersecting point of diagonals 4 C Sr Super60 All Space for rough work Page 5 Chaitanya IIT Academy 6kPq 3 20 06 2021 Sr Super60 All Jee Adv 2018 P1 GTA 11 Q P A Resultant electrostatic force on the system of four charges due to dipole is B Resultant electrostatic force on the system of four charges due to dipole is r 6kPq cos

It is claimed that two cesium clocks if allowed to run for 100 years free from an disturbance may differ by only about 0 02 s What does this imply for the accura of the standard cesium clock in measuring a time interval of I s

A uniform disc is performing pure rolling on a smooth horizontal stationary surface with constant angular velocity V R and linear velocity of centre of mass V as shown is fig find the correct statements at the given instant of time Radius of the disc is R Assume A B C D are on the circumference of the disc A D B V Stationary smooth surface C V A Acceleration of the lowest point C of the disc is R B The radius of curvature of the highest of point A of the disc is 4R 2V C The relative acceleration between the highest point A and lowest point C is R D Acceleration of the lowest point C of the disk is zero A plane progressive transversal mechanical wave is advanced in a medium along

pr to be projected on a level ground Its speed of projection remains fixed at u but the angle of projection 0 with horizontal can change from 0 to 90 Plot range on the level ground against 0 3 R R 90 0 2 4 R R 90 0

Calculate F dr for the given data If F is a force this gives the work done by the force in the displacement along C F xv x v 1 C is the quarter circle from 2 0 straight to 0 2 with center 0 0

A satellite has kinetic energy K potential energy U and total K U E energy E The value of will be K U 2 WIN 3 1 2 3 3

Velocity profile for a fluid between two flat plates Voy as shown in figure is given by H which one of the following is FALSE Moving Plate Vo X Fluid H Indicate Fixed Plate a Shear stress is constant in the gap every where and is independent of y b Shear stress acts in the negative x direction on the lower plate c Shear stress acts in the negative x direction on the upper plate

Question No 05 Multiple Choice Select 1 out of 4 options for the question below To get the real image of small size from a concave mirror position of object is Options At focus Between centre of curvature and focus Between infinity and centre of curvature At centre of curvature

A circular road is banked for speed 40 km hr radius of track is r A car of mass m attempts to go on the circular road The friction coefficient between the tyre and the road is negligible i The car can not make a turn without skidding ii For the speed of car less than 40 km hr it will slip down iii If car turns at speed 40 km hr the force by the road N on car is equal to mu where is speed of car iv If car turns at speed 40 km hr the force by the road N on the car is more than mg as well as more than mu Question Type Single Correct Type 1 I II 211 III C LIV

The Sun is a hot plasma ionized matter with its inner core at a temperature exceed 107 K and its outer surface at a temperature of about 6000 K At these h temperatures no substance remains in a solid or liquid phase In what range do expect the mass density of the Sun to be in the range of densities of solids liquids or gases Check if your guess is correct from the following data mass of Sun 2 0 x10 kg radius of the Sun 7 0 x 10 m

In the following figure the speed of incompressible fluid in A pipe of area is 4 A 3 3 m s A 4 m s 10 m s 20 m s 5 m s 15 m s A 4

It takes one minute for a passenger standing on an escalator to reach the top If the escalator does not move it takes him 3 minute to walk up How long will it take for the passenger to arrive at the top if he walks up the moving escalator

An insect is moving uniformly at speed 2cm s on outer surface of a vertical right circular cone Without changing its sense of motion about axis of cone it completes a round trip and reaches to starting point A in minimum time Given Apex angle of cone 60 Height of cone 3cm A A A time taken is 2 sec B time taken is 2 3 sec C magnitude of acceleration of insect first increases then decreases

A pump motor is used to deliver water at a certain rate from a given pipe To obtain twice as much water from the same pipe in the same time the power of motor has to be increased to Question Type Single Correct Type 1 2 times 2 4 times 3 8 times A 16 times

A biker starts a race and crosses the half line in 3 second with speed 54 km h and after that he increases his speed uniformally at a rate 7 5 m s and completed the race in 5 second A Acceleration in the first half of the race is 5 m s B He finished the race with speed 108 km h C Acceleration in the second half of the race is 12 5 m s Choose the correct option O Only A O Both B and C O Both A and B

32 If in a plano convex lens radius of curvature of convex surface is 10 cm and the focal length of lens is 30 cm the refractive index of the material of the lens will be 1 1 5 2 1 66 3 1 33 4 3

A glass clad fiber is made with core glass of refractive index 1 4 and the cladding is doped to give a fractional refractive index difference of 0 004 Choose the correct options Marks 1 The numerical aperture of the fiber will be OPTIONS 0 00167

a 7N b 33 Three charges of equal magnitude q is placed at the vertices of an equilateral triangle of side 1 The force on a charge Q placed at the centroid of the triangle is 3Qq b 4E 2 2Qq c 4TE 2 d zero Qq 2ne1

8 bjective NCERT B 50 Take the particle in question number electron projected with velocity v 4x 1 ms j electric field between the plates separated by Im 8 2 x 10 NC then the electron will strike the uppe plate if the length of plate is Take m 9 1x10 b 3 9 cm d 3 3 cm a 2 14 cm c 1 23 cm Bectic

65 A circular plane sheet of radius 10 cm is placed in a uniform electric field of 5 x 105 N C making an bb angle of 60 with the field The electric flux through the sheet is a 1 36 x 102 N m C 1 b 1 36 x 10 N m C 1 N m Cl

proton m 1 67 10 27kg is moving at a speed of 6 0 10 6 m s What is the de Broglie wavelength OPTIONS 2 0 10 13 m 0 33 10 13 m

In a photoemissive cell with executing wavelength A the fastest electron has speed v If the exciting wavelength is changed to the speed of fastest emitted electron will be A B Greater than v 4 Correct Answer Your Answer

he wavelength of emission of radiation is 3000A and the coefficient of spontaneous mission is 10 power12 s Given k 8 6x 10 5eV K or 1 38 X 10 power 23 J K Einstein coefficient A21 stands for OPTIONS reciprocal of life time of excited state life time of excited state reciprocal of life time of ground state

A particle of mass m moves in the one dimensional potential V x Fox where Fo is a positive constant a Determine the solution r t for the initial conditions x 0 xo 0 and 0 Deduce that the angular frequency of the oscillations is T Fo 2mxo 1

A wire elongates by l mm when a load W is hanged from it If the wire goes over a pulley and two weights W each are hung at the two ends the elongation of the wire will be in mm 1 l 2 2l 3 zero 4 1 2

Consider a infinitely long charged cylindrical insulator of uniform volume charge density pas shown in the figure There is also a long cylindrical cavity of radius r having its axis parallel to axis of cylindrical charged body X A The magnitude of electric field intensity at the xx axis of charged body is B The magnitude of electric field intensity at axis xx of charged body is zero pr 2 d pd 2 0 C The magnitude of electric field intensity at axis yy of charged body is D The magnitude of electric field intensity at any point in the caivity is Pd 2 0

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