Unit & Dimensions Questions and Answers

A car is moving at a constant speed of 40 km h along a straight road which heads towards a large vertical wall and makes a sharp 90 turn by the side of the wall A fly flying at a constant speed of 100 km h starts from the wall towards the car at an instant when the car is 20 km away flies until it reaches the glasspane of the car and returns to the wall at the same speed It continues to fly between the car and the wall till the car makes the 90 turn a What is the total distance the fly has travelled during this period b How many trips has it made between the car and the wall

Choose the correct statement following 1 Dimensionless quantities can have a unit 2 A dimensionally correct equation must be correct 3 Change in system of units will surely change the numerical value of the physical quantity 4 Dimensions of a physical quantity can never be a fraction

36 If A 21 31 and B 41 61 2k then the angle between A and B is a 45 c 000 b 690 d none

30 of the resistors shown in figure 32 E11 has a resistance of 10 2 and each of the batteries has an emf of 10 V Find the currents through the resistors a and b in the two circuits a a b a E11 E2 Figure 32 E11 36 Find the potential difference V V in the circuits shown in figure 32 E12 H R3 a R R a b b b a b R2

A closed loop carrying current i is placed so that its plane is perpendicular to the long current carrying straight conductor as shown in the figure The net force acting on the loop is where WZ and XY are circular arcs H 40 Sortio w 1 Zero 2 5000 3 CO Moi i b a 2 ab Molio a b b a X N 22 2 Mot 27 BW x B B w x dx b M

In a simple pendulum length increases by 4 and g increases by 2 then time period of simple pendulum 1 Increases by 4 2 Increases by 3 3 Decreases by 3 4 Increases by 1

ABCDEF is a regular hexagon with point O as center The value of AB AC AD AE AF Pis 1 2AO 2 4AO 3 6AO 4 0

A particle of mass m is executing oscillation about the origin on the x axis Its potential energy is U x K x 3 where k is a positive constant If the amplitude of oscillation is a then its time period Tis Eska 2 2 1 2mv 1 alf K 3Kx 2 tom 3k ma Proportional to 2 Proportional to a 3 3 Proportional a

A physical quantity of the dimensions of length that can be e formed out of c G and is c is velocity of light G 4 0 is universal constant of gravitation and e is charge 2017 200 G a e 4 EO 71 2 71 2 0 4 42 102 1 e G47 b c 648 G d G e 71 2 C 47 E

Consider a simple pendulum having a bob attached to a string that oscillations under the action of force of gravity Suppose that period of oscillations of the simple pendulum depends on its length I mass of the bob m and acceleration due to gravity g Derive the expression for the time period using method of dimensions

We measure the period of oscillation of a simple pendulum In successi Measurements the readings turn out to be 2 63 S 2 56 S 2 42 S 2 71 and 2 80 S Calculate the absolute errors relative error and percentag

A weight W rests on rough horizontal plane If the angle of friction be 0 then calculate the least horizontal force that will move the body along the plane Osnca let

6 A physical quantity x depends on quantities y and z as follows x Ay B tan Cz where A B and C are constants Which of the following do not have the same dimensions a x and B c y and B A b C and z 1 d x and A

28 A physical quantity is a physical property of a phenomenon body or subs by measurement 34 The magnitude of the components of a vector are to be considered dimensionally distinct For example rather than an undifferentiated length unit L we may represent length in the x direction as L and so forth This requirement stems ultimately from the requirement that each component of a physically meaningful equation scalar or vector must be dimensionally consistent As an example suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity V and of width D and he is swimming in direction perpendicular to the river flow with velocity V relative to river L T assuming no use of directed lengths the quantities of interest are then V V both dimensioned as S the drift and D width of river both having dimension L With these four quantities we may conclude that the equation for the drift S may be written So VaVbDc y Or dimensionally L x L from which may deduce that a b c 1 and a b 0 which leaves one of these exponents undetermined If however we use directed length dimensions then V will be dimensioned as Ly V as S as L and D as L The dimensional equation T T becomes L a b and we L and we may solve completely as a 1 b 1 and c 1 The increase in deductive power gained by the use of directed length dimensions is apparent Which of the following is not a physical quantity A Height of a boy C Fever of a boy A R 29 From the concept of directed dimension what is the formula for a range R of a cannon ball when it is fired with vertical velocity component V and a horizontal velocity component V assuming it is fired on a flat surface Range also depends upon acceleration due to gravity g and k is numerical constant k V V g B R B Weight of a boy D Speed of a running boy k V g R C R k V Vyg D R k V V g

In the figure shown the blocks A C are pulled down with constant velocities u Acceleration of block B is GF V A tan 0 sec 0 b C 1 2 b sec 0 tan 0 B 2 u b tan 0 DXzero A b 010 B b C

8 If percentage error in the measurement of radius of the sphere is 1 5 then the maximum percentage error in measurement of its volume is 1 3 3 4 5 2 1 5 4 6

A physical quantity P is related to four observables a b c and d as follows P The percentage errors of Vcd measurement in a b c and d are 1 3 4 anc 2 respectively What is the percentage error in the quantity P

In a screw gauge the graduation in the circular scale consists of 100 equal divisions and 10 complete rotation of the cap is equivalent to 5 mm on the main scale While measuring diameter of a wire with screw gauge a particular observation gives initial circular cap reading as 57 and after completing 3 complete rotation the final circular cap reading as 63 It is observed that while proceeding from initial reading to final reading the cap reading increases Calculate the diameter of the wire from the above data

If the radius of the earth be increased to a factor of 5 then by what factor its density be reduced to keep the value of the acceleration due to gravity on the surface same 1 3 1 25 1 55 est 5 JAY 5

A dip needle vibrates in a vertical plane perpendicular to the geographical meridian The time period of vibration is found to be 2 second The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be 2 second If the angle of declination is 60 then the true angle of dip is v 1 tan 1 3 45 1 2 2 tan 2 T 22 timbe tan 2

If the four forces as shown are in equilib press F F in unit vector form F 15 N 37 30 30 10 N

the values of two resistances are and R 10 0 0 1 The when they are connected in parallel In an experiment R 5 0 0 2 total resistance is a 3 3 7 c 3 4 7 b 3 3 5 d 2 5 7

Fill in the blanks for Sonometer 1 In sonometer if tension of wire and length of wire becomes double and mass per unit length of wire remain constant then fundamental frequency of wire will becomes of wire and length becomes double and mass of wire remain constant then

The distance at which average radius of the earth orbi subtends an angle of 1 arc second is b Astronomical unit d Unified atomic unit J KC a Parsec c Light year

D Dimensional formula of universal gravita constant 1 M L T r 2 M LT co pripra 26 Hal yarala 1 M L T 3 IM 1 1 1441146 961 1941943 2 M LT 4 ML T 1

your understanding of the vectors material covered in the course so far Use these quantities to demonstrate your learning of the topics listed below It will be up to you to clearly define the topics covered and to create your own questions Make sure that every solution includes at least one of the given vectors scalars or units Include additional Information as needed Some topics to include are Meaning of a vector Geometric vectors Magnitude of a vector Scalar multiplication of a vector Addition subtraction of vectors Properties of addition subtraction scalar multiplication of vectors Applications of vectors forces and velocity Vectors 76 km h N32 W 102 N down Scalars 24 706 Units N km h

Question 24 The unit of coefficient of friction is N kNm no unit Pascal

Question 18 Out of followings which is not vector quantity Force Speed Displacement Acceleration

240 A particle of mass 2 kg is moving in circular path with constant speed 10 m s The change is magnitude of velocity when particle travels from P to Q will be assume radius of circle is 10 ali to elvons moling n 30 Lesignado tols lonls AV P 1200 20 instendo al potom ielnoshod s no noitem elitbejme not epas A loups apfosire to sprc tot maclo 1 10 3 2 20 3

O 32 V F is force and V is velocity List l 1 11 B a Q L T III 3 R ML IV a S T U a P Speed of light undefined Force momentum Which of the following combination is correct Q II T O III III P List Il

Let a vector ai B be obtained by rotating the vector 31 by an angle 45 about the origin in counterclockwise direction in the first quadrant Then the area of triangle having vertices a 3 0 and 0 0 is equal to 1 3 2 1 4 2 2

The maximum height attained by a projectile is increased by 10 keeping angle of projection constant What is percentage increase in time of flight 10 5 20 min sec 18

Time period of oscillation of rain drop depends on surface tension S density p and radius r Then time period T is Proportional to p Proportional to Proportional to Proportional to 19 100 310

If P is radiation pressure c represents speed of light and Q is radiation energy striking a unit area per second then non zero integers x y and z such that PXQYCZ is dimensionless are A x 1 y 1 z 1 B x 1 y 1 z 1 C x 1 y 1 z 1 D x 1 y 1 z 1

A Fill in the blanks 1 The quantities which are unique and do not depend on other quantities are called 2 3 4 5 6 quantities Decametre is of metre kg is equal to 1 tonne of an object can be determined using graph paper clock is used to measure smaller time intervals is used to measure the temperature of an object

Q 16 A current of 2 5 0 05 A flows through a wire and develops a potential difference of 10 0 1 volt Resistance of the wire in ohm is A 4 0 12 B 4 0 04 O O O O A B O C D C 4 0 08 D 4 0 02

For the system shown in figure the pulleys 130 are light and frictionless The tension in the string will be 0 m 2 A mgsine C 2mgsin0 3 B mgsin0 1 D mgsin0 2 m 131 132

126 The relative density of the material of a body is the ratio of its weight in air and the loss of its weight in water By using a spring balance the weight of the body in air is measured to be 5 000 05 N The weight of the body in water is measured be to 4 00 0 05 N Then the maximum possible percentage error in relative density is A 11 C 9 B 10 D 7 1

A cylindrical tube L 125 cm is resonant with a tuning fork of frequency 330 Hz If it is filling by water then to get resonance again minimum length of water column is Vi 330 m s air A 50 cm C 25 cm B 60 cm D 20 cm

The truck left city A for city B at a speed of 40 km h and 45 minutes later the car left A for the same direction at a speed of 60 km h which reached city B and returned to city A The car met the truck for the second time on the way back which had to cover 20 km before reaching city B How many minutes after its departure did the car meet the truck for the

A parallel plate capacitor of area A plate separation d and capacitance C is filled with four dielectric materials having dielectric constant k k k and k as shown in the figure If a single dielectric material is so be used to have the same capacitance C in this capacitor then its dielectric constant k is given by NEET 2016 A 3 A 3 1 k k k k 3k 3 2 3 kk k k k 3 k KA 2 k 1 k3 A13 T d 2 k k k 2k 1 1 1 kk k k 2k4

radiation of photon energy 1 Two 12 Three Accrding to Bohr s 3 Four 4 One AD When photons of energy hv fal on an aluminium plate of work function E photoelectrons of maximum kinetic energy K are ejected If the frequency of the radiation is doubled the maximum kinetic energy of the ejected photo electrons will be AIPMT 2006 1 K E 2 2K voton of energy 3 K Me Y is kg m s will be 4 K hv AIPMT 2006

1 5 x 1020 2 6 1018 3 62 x 10 0 4 An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level The velocity that the atom acquired as a result of photon emission will be m is the mass of the electron R Rydberg constant and h Planck s constant AIPMT Pre 2012 4 24 hR 25m 2 25 hR 24m 3 24 m 25hR rogon atom jumps from first excited to the ground state 25 m 24hR 4

The displacement of a progressive wave is represented by y Asin kx ot where x is distance and t is time The dimension of w k is same those of Angular wave number Frequency Amplitud e Speed

A car of mass m starts from rest and accelerates so that the instantaneous power magnitude P The instantaneous velocity of this car is proportional to 1 t P 3 1 2 2 1 2 AIPMT Mains 2012 4 Jm kg Hence the particle is displaced from posita

7 893 gram of a substance occupies a volume of 1 1 cm The density c substance with appropriate significant figures is 07 18 g cm 3 O 7 20 g cm 3 7 2 g cm 3 O 7 175 g cm 3

49 Figure a shows a ring of mass m and figure b shows half portion of the same ring Gravitational field at point P in figure b is I2 in magnitude and makes an angle o with line AB Gravitational field at point P in figure a is I in magnitude The ratio of It is 212 a sec o A P a b cos p 12 b c tan o A P B d sin o

A force is given as F a B vis velocity Then dimensional e 1 ML T 2 3 M L T 4 where F is force formula of a B 2 is 2 M L T 2 4 M L T 2

Q 31 The area and volume of sphere is 4 50 0 10 cm2 and 50 30 0 10 cm3 Calculate total percentage error in the measurement of area and volume of sphere a 2 4 b 2 42 c 2 424 d 2 4245 Q 32 Which one of the following units is a fundamental unit a watt b joule sec c ampere d newton

The time of reverberation of a room A is one second The time in seconds of reverberation of a room having all the dimensions double of those of room A is 1 s 2 s 3 s