Unit & Dimensions Questions and Answers

5 Radius of current carrying coil is R Then ratio of magnetic fields at the centre of the coil to the axial point which is R 3 distance away from the centre of the coil 1 1 1 2 1 2 3 1 4 4 8 1

The speed of light C gravitational constant G and planck s constant h are taken as fundamental units in a system the dimensions of time in this new system should be 1 G1 2 h1 2 C 3 2 2 Gh c a 3 G 2 h1 2 C 3 2

A particle A having a charge of 2 0 x 10 6 C and a mass of 100 g is placed at the bottom of a smooth inclined plane of inclination 30 Where should another particle B having same charge and mass be placed on the incline so that it may remain in equilibrium 1 16 cm 2 27 cm 3 24 cm 4 47 cm

3 A calorie is a unit of heat or energy and it equals about 4 2 J where 1J 1 kg m s Suppose we employ a system of units in which the unit of mass equals a kg the unit of length equals m the unit of time is ys Show that a calorie has a magnitude 4 2 ay in terms of the new units

answer 2 The physical quantity Absorbed dose index has th Sl unit of 1 Becquerel 10 2 Henry 4 Gray

4 A dimensionless a never has a unit c may have a unit quantity b always has a d does not exist

Round off the following numbers as indicated 15 654 upto 3 digits 1426 upto 5 digits 5 996 10 upto 3 digits 0 06218 upto 4 digits 2 663 upto 3 digits i ii iii iv V

3 A projectile is fired at an angle of 45 with the horizontal Elevation angle of the projectile at its highest point as seen from the point of projection is AIPMT Mains 2011 1 tan 1 3 60 3 2 2 45 4 tan 1 1 2

The resultant of two vectors at an angle 150 is 10 units and is perpendicular to one vector The magnitude of the smaller vector is 2 10 3 units 4 5 3 units 1 1 10 units 3 10 2 units

In dimension of critical velocity ve of liquid following through a tube are expressed as npr where n p and r are the coefficient of viscosity of liquid density of liquid and radius of the tube respectively then the values of x y and z are given by 2015 Re a 1 1 1 c 1 1 1 b 1 1 1 d 1 1 1

B Speed of a running boy 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 components and a hoceteraal velocity component V assuming it is fired on a flat surface Range also depends upon acceleration due to gravity g and k is numerical y constant A R k V V g B R k V g C R k V V 8 D R k V Vo

A wire of fixed length is wound on a solenoid of length and radius r Its self inductance is found to b Now if same wire is wound on a solenoid of length 2 1 2L 2 A 3 and radius 3L 2 then self inductance will be 4 AI

2 Force F is given in terms of time t and distance x by F A sin Ct B cos Dx A Then the dimensions of and are given by B a MLT 2 MOLOT c MOLOTO MOLT b MLT 2 MOL TOJ d MOLT MOLOTO

19 A bullet of mass 0 25 kg is fired with velocity 302 m s into a block of wood of mass m 37 5kg It gets embedded into it The block m is resting on a long block m and the horizontal surface on which it is placed is smooth The coefficient of friction between m and m is 0 5 Find the and displacement of m on m and the common velocity of m m Mass 1 25 kg m

4 secx tanx secx tanx A 2 sec x sec x tan x C 2 sec x sec x tan x If y d dy then dx equals B 2sec x sec x tan x D 2 sec x sec x tan x

The period of oscillation of mercury of mass m and density p poured into a bent tube of cross sectional area S whose right arm forms an angle 0 with the vertical as shown in figure is A 2T m VpS 1 sine g C 2 444444444444 S 1 0 m WWW TH m VpS sin eg B 2T D 2 m

71 If a and b are noncollinear then x yb 0 implies 1 x 0 y finite 2 y 0 x finite 3 x 0 y 0 4 None of these

3 Resistance of a conductor is given as R A The symbols have their usual meanings Select correct option 1 Expression is dimensionally inconsistent 2 Expression is correct 3 Expression cannot be derived using dimensional analysis 4 Both 2 3

If the radius of cross section of the conductor is increased by 0 1 keeping volume constant then percentage change in the resistance of the conductor is 1 0 2 3 0 3 2 0 1 4 0 4

In an experiment the percentage of error occurred in the measurement of physical quantities A B C and D are 1 2 3 and 4 respectively Then the maximum percentage of error in the measurement X where X 1 2 3 4 10 3 13 16 10 A B 2 C D Error tutab 2 will be Chapter il mete

Example 3 The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass m velocity v and radius r of the circle Derive the formula for using the method of dimensions

A tritium gas target is bombarded with a beam of monoenergetic protons of kinetic energy 3 MeV The K E of the neutron emitted at 30 to the incident beam is K Find the value of K approximately in whole number Atomic masses are H 1 007276 amu n 1 008665 amu H 3 016050 amu He 3 016030 amu

7 A circular platform is mounted on a frictionless vertical axle Its radius R 2 m and its moment of inertia about the axle is 200 kg m It is initially at rest A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms relative to the ground Time taken by the man to complete one revolution is 1 IS AIPMT Mains 2012 3 2 2 TU S

The circular scale of a micrometer has 200 divisions and pitch of 2mm Find the measured value of thickness of a thin sheet mm 6 In 0 10 1 3 41 mm 1 3 3 3 46 mm 2 4 3 50 40 6 41 mm 3 51 mm Twx 48 3 0 V 3M 4M K E

Standing on an icy surface a man of mass 60 kg throws a stone of mass 3 kg horizontally at a velocity of 8 m s How far does he slide back if the coefficient of sliding friction between the man and the icy surface is 0 02 41 cm

The length of thin wire required to manufacture a solenoid of inductance L and length if the cross sectiona diameter is considered less than its length is 1 TLI 2 0 2 4TLI V Mo 3 2TLI V Mo 4 TLI Mo

Solve with due regard to significant figures 4 0 4 0 x 10 2 5 x 10 6 2 125 653 0 9996 3 523 7 x 6 27 x 1 758 7 x 10

the numerical We have value of physical quantity from one system of units into the other system into EXAMPLE 1 12 Convert 76 cm of mercury pressure Nm 2 using the method 18 dimensions of

Question no 41 to 43 certain system of absolute units the acceleration produced by gravity in a body falling freely is denoted by 5 the kinetic energy of a 500 kg shot moving with velocity 400 metres per second is denoted by 2000 its momentum by 100 The unit of length is A 15 m B 50 m The unit of time is A 10 s The unit of mass is A 200 kg B 20 s B 400 kg C 25 m 9 5 s C 800 kg D 100 m D 15 s D 1200 kg

Refractive index of a glass as light ray passes from air to glass is given by n experiment i and r were found to be 45 3 and 30 3 then error in n is nearly sinr A 0 28 C 0 15 B 0 20 D 0 143 otellite mo

344 ata artik Ag 9 34 34 5600 km 3446 5 t yeaf 1 7 2 x 10 0 J 3 8 5 x 1010 J 1600 km 6400 km 2 7 8 10 0 J T MRI 4 5 6 10 0 J

38 Two vectors A and B are defined as A ai and B a cos oti sinot where a is a constant and rad s If A B 3 A B at time t t for the first time the value of t in seconds is

9 Four charges equal to Q are placed at the four corners of a square and a charge q is at its centre If the system is in equilibrium the value of q is AIEEE 2004 2 1 2 2 c b 1 2 2 4 1 2 2 4 1 2 2

sto write Read the following paragraph carefully underline all adjectives and the other degrees of comparison for them Yesterday we went for a picnic to Nehru Zoological Park which is one of the biggest

3 B The angle between vectors 1 90 63 3 0 and i k is s i and i 1 2 180 4 60 actors

1 A physical quantity of the dimensions of length that can be formed out of c G and e is c is velocity of light G is universal 4TEO constant of gravitation and e is charge a 1 1 c 1 2 G 4 TEO 2 2 e 1 2 71 2 e 6470 b c G d G 1 2 NEET 2017 71 2 e

Count total number of significant figures in the following measuremen a 4 080 cm 4 d 10 00 cm 4 6 0 079 m a 46 4 07080 G c 950 A 07 090 10 4

Consider hypothetical wave pulse given by the following y 0 x 0 y x 2 y 3 x A C y 0 The pulse travels leftwards negative x direction at speed v 2m s Which of the following plots are correct 1m meter in m 2 x20 32x22 x 3 1 1 2 0 1 2 3 2 t second at t 0 at x 0 x in m at time 1 0 y x in meter v 1 D m s H B 1 1 2 in m s 1 1 2 1 2 1 14 4 at x 0 3 2 7 t second at t 0 13 x in m

33 A charge particle moves along the line AB which lies in the same plane of a circular loop of conducting wire as shown in the fig Then A B 1 No current will be induced in the loop 2 The current induced in the loop will change its direction as the charged particle passes by 3 The current induced will be anticlockwise 4 The current induced will be clockwise

9 Two vectors A and B have equal magnitudes The magnitude of A B is n times the magnitude c A B The angle between A and B is 2 n 1 A 2 n A sin 1 B cos 1 1 C cos 1 n n 1 JEE Main 2019 Online h 1 D sin 1

The dimensions of the quantity kinetic energy designated by K are kg m s It can be written in terms of the momentum p and mass m as K p 2m a What are the units of momentum in terms of fundamental SI units Use the following as necessary kg m and s kg Your answer cannot be understood or graded More Information p b Force is measured in units of newtons N where 1 N 1 kg m s2 What are the units of momentum p in terms of a newton and another fundamental SI unit Use the following as necessary N m and s p N S Your answer cannot be understood or graded More Information X p kg c What If Physicists often measure the momentum of subatomic particles moving near the speed of light in units of MeV c where c is the speed of light and 1 MeV 1 6 x 10 13 kg m s Based on this what are the units of momentum for a high speed subatomic particle in terms of fundamental SI units Your answer cannot be understood or graded More Information m X What are the units of momentum for a high speed subatomic particle in terms of a newton and another fundamental SI unit p N S Your answer cannot be understood or graded More Information X

A magnet is dropped down in an infinitely long vertical copper tube Then 1 The magnet moves with continueously decreasing velocity and ultimately comes to rest 2 The magnet moves with continueosly increasing velocity and ultimately acquires a constant terminal velocity 3 The magnet moves with continueously increasing velocity and acceleration 4 The magnet moves with continueously increasing velocity but constant acceleration

In the measurements least number of signifi the result will also be rounded off to one decimal place Example 5 A thin wire has a length of 21 7 cm and radius 0 46 mm Calculat the volume of the wire to correct significant figures Solution Given 1 21 7 cm r 0 46 mm 0 046 cm

A physical quantity of the dimensions of length e 4 0 that can be formed out of c G and velocity of light G is universal gravitation and e is charge 1 G 2 1 e 2 2 41EO 1 1 2 2 2 c G 1 is c is constant of NEET 2017 1 2 e 2 4TEO 2 D

Prob 1 If a copper wire is stretched to make it 0 1 longer the percentage change in its resistance A 0 2 increase B 0 2 decrease C 0 1 increase D 0 1 decrease ol For a given wire R So that R p AR R 2 AL L V PL S with L x s volume V constant 2 0 1 0 2 increase

An isolated particle of mass m is moving in a horizontal plane x y along the x axis at a certain height 3m 4 m above the ground It suddenly explodes into two fragments of masses 4 and 15 cm The larger fragment at this instant is at B y 20 cm C y 5 cm smaller fragment is at y A y 5 cm In which of the following cases the centre of mass of a rod may be at its centre An instant later the D y 20 cm

3 B 60 C 90 D 120 The vector sum of 6 coplanar forces each of magnitude F when each force is making an angle of 1 3 with the preceding it is A F B 6F C 3F 2 D zero The following sets of three vectors act o

The electric field is given by E 1 By Cz X The SI units of A B anc C are respectively 1 N m V m N m C C 2 V m V m N m C 3 V m V m N C m 4 V m N m C N C m

Dimensional Analysis 1 Unit Conversions Question 7 Converting from one unit to another happens when companies use different measurement systems In Europe the acceleration due to gravity on Earth is 9 8 meters per second squared 9 8 m s 2 In some companies in the USA the same acceleration is 32 feet per second square 32 ft s 2 Which choice below shows the correct conversion between European and American units Assume there are 3 28 feet in one meter Select one 08m L 30 1

You are a sports agent s assistant You are preparing a report on contracts you have obtained for the agent s clients You recently negotiated the following annual contracts 2 8 million 18 9 million 1 5 million 1 2 million 1 5 million and 3 5 million per year The standard deviation of the data is 6 3 and the range is 17 7