Unit & Dimensions Questions and Answers

A brass rod at 30 C is observed to be 100 cm long when measured by a steel scale which is correct at 0 C If a for steel is 12 x 10 6 C and of brass is 19 x 10 6 C the correct length of brass rod at 0 C is 1 100 021 cm 3 100 042 cm 2 99 979 cm 4 99 958 cm

Laws of Motion 65 The contact force between surface and mass in the given figure is g 10 m s 20 N 2 kg 1 20 N 31 30 N 10 2 20 2N 4 Zero

Note In stating numerical answers take care of significant 2 1 Fill in the blanks a The volume of a cube of side 1 cm is equal to m b The surface area of a solid cylinder of radius 2 0 cm and h 1076 mm 4008 mnt c A vehicle moving with a speed of 18 km h covers m L d The relative density of lead is 11 3 Its density is c Fill in the blanks by suitable conversion of units a 1 kg m s g cm s b 1 m ly 2 2 2 3 w EXERCISES c 3 0 m s 2 km h d G 6 67 x 10 N m kg cm s g EOS A calorie is a unit of heat energy in transit and it equals 1 kg m s 2 Suppose we employ a system of units in which kg the unit of length equals m the unit of time is y s S magnitude 4 2 a 3 2 y in terms of the new units 4 Explain this statement clearly To call a dimensional quantity large or small is meaning standard for comparison In view of this reframe the follow necessary a atoms are very small objects b a jet plane moves with great speed c the mass of Jupiter is very large d the air inside this room contains a large number of mo e a proton is much more massive than an electron f the speed of sound is much smaller than the speed of li A new unit of length is chosen such that the speed of light is the distance between the Sun and the Earth in terms of 8 min and 20 s to cover this distance Which of the following is the most precise device for meas a a vernier callipers with 20 divisions on the sliding scale b a screw gauge of pitch

A wire has a mass 0 3 0 003 g radius 0 5 0 005 mm and length 6 0 06 cm The maximum percentage error in the measurement of its density is Tough a 1 b 2 c 3 Nut d 4 a ax c ax 47 The pitc

Illustration 14 The side of a cube is 2 00 0 01 cm The volume and surface area of cube are respectively 1 8 00 0 12 cm 24 0 0 24 cm 3 8 00 0 04 cm 24 0 0 06 cm 2 8 00 0 01 cm 24 0 0 01 cm 4 8 00 0 03 cm 24 0 0 02 cm Solution

20 The shortest length of a resonance tube which resonates with a fork of frequency 256 is 32 cm The corresponding length for a fork of frequency 384 is 20 8 cm What is the end correction A 1 6 cm C 0 8 cm THOR B 3 2 cm 4 QAR A D 2 cm

Paragraph X In an experiment to determine charge to mass ratio of electron using a cylindrical diode we use following equations 8V mr B V potential difference across diode of radius r i B magnitude of critical magnetic field when electron pass undeviated ii B Honl 1 D 1 n number of turns per metre length of solenoid I current in solenoid D diameter of solenoid and L length of solenoid Experimental observations are n 3920 turns in 1 m D 0 035 0 001 m L 0 120 0 001 m r 34 0 1 x 10 m I 1 92 0 02 A and V 20 1 V 15 Error occurred in magnitude of magnetic field is a 1 b 2 c 3 16 Error in value of e m of electron is a 2 b 4 c 6 d 4 d 8 Paragraph A A thick spherical shell of charge Q and uniform volumetric charge density p has inner and outer radii and respectively Take potential at infinity is zero also r and r 3r 17 Potential at a point distant 2r from centre is a 15 pr E b 25 pr 0 c 3 5 pr Ep d 45 pr Ep b 2pr d 4 pr Eo 18 Potential at a point inside the shell at distance 0 5 r from centre is a pr E c 3 pr 1

7 A physical equation is given by v a 4 e Bx where v is speed x is displacement and t is time S I unit of will be 1 MLT 2 2 M T L 3 MOL T 2 4 M L T

Derive Stoke s law formula for the viscous f orce acting on a spherical ball moving through a viscous fluid The viscous force F acting on the sphere depends on i n the viscosity of the liquid ii r the radius of the sphere iii v the velocity of the sphere given K 6

The respective number of significant figures for the num bers 23 023 0 0003 and 2 1 x 10 are AIEEE 2010 1 4 4 2 3 5 1 5 2 5 1 2 4 5 5 2

35 The radius of a sphere is 5 3 0 1 cm The percentage erro in its volume is a c 0 1 5 3 x100 0 1 100 3 53 0 1 b 3xx100 5 3 GROONST 0 1 d 3 100 5 3

10 Which of the following measurement is most precise a 5 00 mm b 5 00 cm c 5 00 m d 5 00 km

A bus accelerates uniformly from rest and acquires a speed of 72 km hr in 20seconds The accelearation of the bus is 1 10 m s iola stor 2 5 m s from ifa 3 2 m s 4 1 m s amation It travola o distance v in the first two seconds

If vectors 2 cot cos oti sin otj and B cos sin 2 2 are functions of time then the value of ta which they are orthogonal to each other is 1 t 0 TC 2 t T 4w TT 3

5 A bus travels the first one third distance at a speed of 10 km h the next one third distance at a speed of 20 km h and the next one third distance at a speed of 30 km h The average speed of the bus is 50 a 20 m s 1 b 11 180 d 30 m s 1 11 c ms 1 ms 1

4 The density of a material in CGS system of units is 4g cm In a system of units in which unit of length is 10 cm and unit of mass is 100 g the value of density of material will be a 400 c 0 4 b 0 04 d 40

142 The velocity of light c Planck s constant h and gravitational constant G are taken as the fundamental units How will you express mass in terms of the dimensions of these units NCERT a m c m ch 10 b m 11 d m ols hG

5 The velocity of a freely falling body is a function of the distance fallen through h and acceleration due to gravity g Show by the method of dimensions that v K gh d of dimensions derive an expression

Fv B Find the dimensions of a and B loge 2 v 2 where F force v velocity

24 If in a hypothetical system the unit of velocity is 4 m s the unit of acceleration is 24 m s2 and the unit of force is 6 N then the unit of energy is 1 4 J 2 6 J 3 8 J 4 10 J

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 3 13 A B 2 CXD 2 16 will be NEET 2019

Two similar conducting balls having charges q and q are placed at a separation d from each other in air The radius of each ball is r and the separatio between their centres is d d r Calculate th capacitance of the two ball system 1 9 X X X X 1 4 or 3 4 loge Eor X xxx d 2 2 r 4 4 loge

24 From the dimensional consideration which following equations is correct 1 T 2n R 2 T 2 Gm 3 T 2T 2 Gm 2 R AT Gm 3 R R

e moon is observed from two diametrically extremes A and B on earth The angle of parallax ound to be 1 54 If the diameter of the earth is about 1 276 x 107 m estimate the distance ne moon from the earth

If the error in the measurement of radius of a sphere is 2 then the error in the determination of volume of the sphere will be 1 8 2 2 3 4 4 6

Light enters at an angle of incidence in a transparent rod of refractive index For H what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence CBSE AIPMT 1998 d 13 blu 1 c u 11

3 If electronic charge e electron mass m speed of light in vacuum c and and Planck s constant h are taken as fundamental quantities then permeability of vacuum p can be expressed in urits of 2015 a hc 2 me b h 2 ce 8

The function sin t represents 1 a periodic but not simple harmonic motion with a period 2 w 2 a periodic but not simple harmonic motion with a period w 3 a simple harmonic motion with a period 2 w 4 a simple harmonic motion with a period w

In ancient time different system of units was followed In which unit of mass was ser un of length was gaj unit of time was kaal 1 ser 900 gm 1 gaj 90 cm 1 kaal 3 hr 7 A ball of mass 9 kg is moving with velocity 10 m s Then its momentum mv in ancient syster will be A 1 2 x 106 ser gaj kaal B 10 6 1 2 ser gaj kaal C 1 2 x 106 ser gaj kaal D 120 ser gaj kaal 8 The unit of volume of water in the ancient system will be

Q10 The B is value of A B RPET 1991 2002 BHU a 0 b A B

13 Number of significant figures in the given number 62 00 m is 1 2 3 4 2 3 4 None of these

2 dx S where x represents position and A B x X and B are unknown quantities then dimensions of If A B are 1 MOLTO 3 MOL 1T0 2 MOLOTO 4 MOL T

body moves along the curved path of a quarter rcle Calculate the ratio of distance to displacement 1 11 7 2 7 11 3 11 2 x 7 4 7 11 2

Time period T of a small drop of liquid due to surface tension depends on density p radius r and surface tension s The relation is pr 1 Tr 2 T prs

27 If L and R denote inductance and resistanc respectively then the dimension of L R is cate 1 MOLOT 1 2 MOLOT 3 MOLOT

The following observations were taken for determining surface tension T of water by capillary method Diameter of capillary d 1 25 102 m rise of water h 1 45x102m Using g 9 80m s and rhg x10 N m the 2 the simplified relation T possible error in surface tension is closest to JEE Main 2017 Offline b 2 4

In the figure shown battery 1 has emf 6 V and internal resistance 1 2 Battery 2 has emf 2V and internal resistance 32 The wires have negligible resistance What is the potential difference across the terminals of battery 2 Hw 302 with DOSY

21 The potential energy of a particle varies with distance x from a fixed origin as A x x B U 3 where A and B are dimensional constants then dimensional formula for AB 1 ML T 2 3 M L 9 2T 2 2 ML11 2T 2 4 ML13 2T 3

sphere about its diameter What is the dimensional gyration Central Schools 14 formula of radius of

The vector sum of 6 coplanar forces each of magnitude F when each force is making an angle of with the preceding it is A F B 6F C 3F 2 D Zero

The adjacent graph shows the extension Al of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end If the cross sectional area of the wire is 10m calculate the young s modulus of the material of the wire 1 2x10 N m 2 8 10 m 20 40 60 80 WIN 2x10 N m va 3x10 2 N m 4 2x10 N m

1 Which of the following is the unit of molar gas constant a JK mol 1 c JK 1 PV MT b joule d Jmol l 10

22 The velocity of a particle is given by v A cos t kx where x is position and t is time The dimensions of 1 LT 1 3 L T 2 k is 2 L 1T 4 L T

Dimensional analysis 1 If the units of energy force and velocity are 50 J 5 N and 2m s what will be unit of mass length and

The time period T of a spring mass system depends upon mass m spring constant k length of the spring Force 1 k Find the relation among T m k using dimensional method length

A particle of mass m attached to the end of string of length is released from the horizontal position The particle rotates in a circle about O as shown When it is vertically below O the string makes contact with a nail N placed directly below O at a distance h and rotates around it For the particle to swing completely around the nail in a circle 3 1 h 5 3 h 1 N h 2 h l 5 2 A h 1

1 35 A thin metal square plate has length 1 When it is heate from 0 C to 100 C its length increases by 1 What is th percentage increase in the area of the plate A 2 00 B 2 02 C 2 03 D 2 01 211

The potential difference across a conductor is v 6 0 0 5 v and the current I 1 2 0 2 A The resistance of the conductor is a 5 0 0 7 22 5 0 1 2 92 c 5 0 0 3 d 5 0 1 0 Q DO The aquivalent

11 If P Q and R are physical quantities having different dimensions which of the following combinations can never be a meaningful quantity P Q R B PQ R PQ R A C PR Q

5 The equation of a stationary wave is 2 ct cos 2x y 2A sin Which of the following statements is incorrect 1 The unit of ct is same as that of A 2 The unit of x is same as that of 2 3 The unit of 4 The unit of 2 c 2 C is same as that of is same as that of 2TX t X