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## VECTOR

A PHYSICAL QUANTITY HAVING BOTH MAGNITUDE AND DIRECTION KNOWN AS A VECTOR QUANTITY.

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## MOTION IN ONE DIMENSION

When a body changes its position with respect to its surroundings in a single direction , then the motion is said to be in one dimension. read more about MOTION IN ONE DIMENSION

## MOTION IN A STRAIGHT LINE –

• State the condition when the magnitude of velocity and speed of an object are equal.

• Under what condition will the distance and displacement of moving object have the same magnitude?

• Which vector can be associated with a plane area? And what is its direction?

• Can the relative velocity of two bodies be greater than the absolute velocity of either? to download complete assignment — MOTION IN ONE DIMENSION
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## UNITS AND DIMENSIONS ASSIGNMENT

Assignment of  UNITS AND DIMENSIONS will help the students practice the chapter well , and improve their numerical  skills in this chapter .

Q 1. Calculate the dimensions of (i) force (f) and (it) impulse (i) in terms of velocity(v) , density (p) and frequency (v) as the fundamental units .

Q 2. If the velocity of light c, gravitational constant G and Plank’s constant h be chosen as fundamental units, find the dimension of (i) mass, length and time in new system.

Q 3. Find the dimensions of a/b in the equations, where P is pressure ,t- time & x distance

P= (a-t2 ) / bx

UNITS AND DIMENSIONS ASSIGNMENT

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## UNITS AND DIMENSIONS ASSIGNMENT 1

UNITS AND DIMENSIONS

ASSIGNMENT
CLASS-11
UNITS AND MEASUREMENTS
1> Find the area of circle of radius 3.458cm up to correct significant figures. 2> Name the physical quantities whose dimensions are same. 3> State the no. of significant fig. in the following (a)0.007 cm (b)2.64 x 1024kg (c)0.2370 cm 4> Which of the following measurement is more accurate and why? (1)5000.0 cm(2)0.0005cm (3) 6.00cm. 5> Are all dimensionally correct equations numerically correct? Give one example. 6> If x=a+bt+ct2 where x is in meters and t is in second, what is the dimensional formula of ‘a’ , and ‘c’. 7> Write the dimensions formula of (1) Planck’s constant and(2) Rydberg’s constant
1>The wavelength ‘λ’ depends mass M of the moving particle its velocity v and planks constant ‘h’ . Show dimensionally the relationship between them.
2>In an experiment the refractive index of the glass was observed to be 1.45, 1.56,1.54,1.44,1.54 and 1.53 . Calculate (1) mean value of the refractive index ;(2) Absolute error ;(3)Fractional error ; (4)Percentage error . Express the result in terms of absolute error and percentage error.
3> If (p+ a/V2) (V-b)=RT where the symbols has their usual meanings, then what is the dimension of a/b .
4. If F= a/ b+√d , where f=force ,d= density , then find the dimension of a and b.
5> The factors effecting the time period (T) of the simple pendulum depends on mass , length and acceleration due to gravity . Deduce the relation for time period of the simple pendulum.
6> To determine acceleration due to gravity ,the time of 20 oscillations of a simple pendulum of length 100 cm was observed to be 40 s . calculate the value of ‘g’ and maximum percentage error in the measured value of ‘g’ .
7> If power P=a-x2/b where x represents displacement find the dimension of a and b. 8> A physical quantity Qis given by Q= A.B3/2/C4D1/2 percentage error in A,B,C,D are 1%, 2%,4%,2% respectively . Find the percentage error in Q.
9>The measured value of length , breadth and height of a block is given as l=12.08+-0.01 cm , b=10.12+-0.01cm . h=5.62+-0.01 cm . Calculate the percentage error in the volume of the block.
10>(a) convert 10 J into ergs . (b) convert 10 N into dyne .
11> A planet moves around the sun , the period of revolution ‘T’ depends upon radius of the orbit ‘R’, mass of the sun ‘M’ and gravitational constant ‘G’, show that T2 α R3.
12>If the length and time period of an oscillating pendulum have errors of 1% and 2% respectively , what is the error in the estimate of ‘g’.

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## State and explain Biot-Savart’s law

In this topic we will discuss about Biot-savart’s law and magnetic field at a point due to finite current carrying wire or conductor.

Biot- Savart law – Biot-Savart’s law explain the magnetic field due to small current carrying element

As we know , whenever the current passes through a conductor magnetic field setup around it  . To find the magnetic field at any point first given by Jean Biot and Felix savart . according to Biot- Savart , magnetic field intensity at any point due to small current carrying element is given  as dB=µ0idl sinθ/r2 .

EXPLANATION- Let us consider a small element of length  ‘dl’ carrying a current I through it  . If dB is the magnetic field at a point r distance away from the element , then according to this law

• dB α I …………………….1
•  dB α dl …………………2
•   dB α sin θ …………….3
•   dB α 1/r2 ………………4

after combining these equations ,we get

dB  α   I dl sinθ/r2
so ,   dB= k I dl sinθ/r2

(Where K= µ0/4Π = 10-7 Wb/ (A m ))

Magnetic field due to straight current carrying wire of finite length –****( derivation is not in syllabus for 12th board examination, but we must know the result )

Suppose  current ‘I’ is flowing through  a wire XY , and we have to find the magnetic field at point ‘P’.as shown in figure .

B =  (µ0I/4Πa)(sinɸ1 + sinɸ2) ,

Special cases – Case-(1) —  When the wire is of infinite length and point P is near the wire in that case                        ɸ1=900 , ɸ2=900 ;

So magnetic field at that point P ,   B =  (µ0I/4Πa)(sin90 + sin90)  =  µ0I/2Πa

Case-(2)–  When the wire is of infinite length and point P is near the  one end of the wire in that case                        ɸ1=900 , ɸ2=00 ;

So magnetic field at the point P ,  B =  (µ0I/4Πa)(sin90 + sin0)  = µ0I/2Πa ;

Case-(3)—If length of the conductor is finite (L) and point P lies on right bisector of conductor , then ɸ12= ɸ ; and sinɸ=L/( 4a2+L2)1/2 .

Then magnetic field B= (µ0I/4Πa)(sinɸ + sinɸ)= (µ0I/4Πa)2sinɸ=(µ0I/4Πa)[ L/( 4a2+L2)1/2];

Direction of magnetic field – The direction of magnetic field through a current carrying wire can be found using right hand thumb rule .

Right hand thumb rule – According to this rule we held the current carrying straight wire in our hand grip of our right hand so that thumbs directed towards the direction of flow of current then the curled finger gives the direction of magnetic field around the conducting wire . As shown in figure.

to see the video on Biot-Savart’s law click on the link given below-

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## What is Ampere circuital law

Ampere circuital law – After the discovery of Oersted and Biot-Savart, Ampere found a useful relation between magnetic field and electric current.     [ In the case of all basic laws of physics , Ampere’s law can’t be derived , its validity is based on the correctness of the result.] . According to Ampere circuital law that the linear integral of magnetic field (B) along a imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium µ0 . for a  long straight current carrying conductor  , magnetic field

B= µ0 I/2ΠR

So,

∫B.dl =   ( µ0 I/2Πr) ∫dl    ( integrate with limit 0 to 2Πr )                                                      = ( µ0 I/2ΠR) × 2Πr = µ0I

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## MAGNETIC EFFECT OF CURRENT

Magnetic effect of currentIf current flows through a conductor setup magnetic field around it is first observed by Oersted in 1820 . After that Biot-savart  established a formula for magnetic field due to small current carrying conductor. Direction of magnetic field can be found using right hand thumb rule . If current is flowing through st. line  and thumb shows the direction of current flowing through it then curled finger gives the direction of magnetic field. If current flowing through a circular coil ,and curled finger shows the direction of current then thumbs gives the direction of magnetic field.

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## UNITS AND DIMENSIONS

These questions will help the students to practice and test himself for the chapter units and dimensions.

But before to solve these objective questions of unit and dimensions students must read the following topics , published by Physics classes by Nayan jha:-

UNITS AND DIMENSIONS

Q1. the correct order in which the dimensions of length increases in the following quantities is :

(i)permittivity  (ii) resistance  (iii) magnetic permeability  (iv)stress

(a)(i),(ii),(iii),(iv)   (b) (iv),(iii),(ii),(i)    (c) (i),(iv),(iii),(ii)       (d) (iii),(ii),(iv),(i)

Q2. the ratio of the dimensions of Plank’s constant and that of moment of inertia is the dimension of :

(a)time    (b)frequency   (c)angular momentum   (d)velocity

Q3. consider the following equation of Bernoulli’s theorem

P+ pv2 +pgh =K (constant )

The dimension of K/P are :

(a)thrust         (b)pressure    (c)angle   (d)viscosity

Q3. Dimensions of electric resistance is :

(a)[ML2T-3A-1]         (b) [ML2T-3A-2]

(c) [ML3T-3A-2]         (d) [ML-1T3A2]

Q4. In a system of unit, if force (F), acceleration (A) and time (T) are taken as fundamental units then the dimensional formula for energy is :

(a) [FA2T]        (b) [FAT2]

(c)[FA2T]         (d)[FAT]

Q5. which of the following is not a unit of young’s modulus ?

(a) Nm-1           (b) Nm-2     (c)dyne cm-2   (d)megapascal

Q6. Out of the following four dimensional quantities, which one qualifies to be called a dimensional constant?

(a)Acceleration due to gravity                   (b)Surface tension of water

(c)Weight of a standard kilogram mass   (d)The velocity of light on vacuum

Q7. SI unit of magnetic flux is :

(a)tesla      (b)oersted    (c)weber      (d)gauss

Q8.Which of the following group have different dimension?

(a)Potential difference, emf, voltage       (b)pressure, stress,  Young’s modulu (c)Heat, energy, work done   (d)Dipole moment, electric flux, electric field

Q10. The unit of electric field is not equivalent to :

(a)J/C     (b)J/cm     (c)V/m    (d)N/C

Q11. If E and B respectively represent electric field and magnetic field, then the ratio E/B has the dimension of:

(a) displacement  (b)velocity    (c)acceleration    (d)angle

Q12. The dimension of  E0E2 , where E0 is permittivity of free space and E electric field, is

(a)[ML2T-2] (b) )[ML-1T-2]  (c) )[ML2T-1]  (d) )[MLT-1]

Q13. The mass and volume of a body are found to be 5.00 ±0.05kg and 1.00±0.05m3 respectively. Then the maximum possible percentage error in its density is :

(a)6%      (b)3%     (c)10%      (d)5%      (e)7%

Q14. In an experiment four quantities a,b,c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows:

P= a3b2/cd

Percentage error in P is

(a)10%      (b)7%       (c)4%     (d)14%

Q15. the dimesion of the quantity E x B, where E  represents the electric field and B the magnetic field may be given as:

(a)[MT-3]     (b)[M2LT-5A-2]                                                                         (c) [M2LT-3A-1]     (d) [MLT-2A-2]

Q16. If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are

(a)[FVT-1]     (b)[FVT-2]                                                                                  (c)[FV-1T-1]     (d)[FV-1T]

Q17. the dimensions of mobility of charge carriers are:

(a) [M-2T2A] (b) [M-1T2A]                                                                                (c) [M-2T3A] (d) [M-1T3A] (e) [M-1T2A-1]

Q18. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formulae of surface tension will be :

(a)[EV-1T-2] (b) [EV-2T-2]                                                                                   (c) [E2V-1T-2] (d) [EV-2T-1]

Q19. Plank’s constant (h), speed of light in volume (c) and Newton’s gravitational constant (G) are three fundamental constants. What is the dimension of length

Q20. Which of the following unit denotes the dimension [ML2/Q2]. Where Q denotes the electric charge.

(a)weber (Wb)         (b)Wb/m2      (c)henry (H)        (d)H/m2

Q21. The magnetic moment has dimension of

(a)[LA]         (b)[L2A]          (c) [LT-1A]           (d)[L2T-1A]

Q22. Surface tension has the same dimension as of :

(a)Coefficient of viscosity      (b)impulse      (c)momentum   (d)spring constant    (e) frequency

Q23. which of the following sets of quantities have same dimensional formulae?

(a) Frequency, angular frequency and angular momentum

(b)surface tension, stress and spring constant

(c)acceleration, momentum and retardation

(d)Thermal capacity, specific heat and entropy

(e) Work, energy and torque

Q24. A physical quantity P=  / d3e1/3 is determined by measuring a, b, c,d  and separately with the percentage error of 2%, 3%, 2%, 1% and 6% respectively. Minimum amount of error is contributed by the measure of :

(a)b        (b)a      (c)d       (d)e   (e)c

Q25. Two forces 5N and 12N simultaneously  act on a particle. The net force on particle is

(a) 17N     (b) 12N     (c) 13N      (d) 7N

Q26. A physical quantity Y= a4b4 / (cd4)1/3 has four observables a, b, c, and d. the percentage error in a, b, c and d are 2%, 3%, 4% and 5% respectively. The error in y will be :

(a) 6%    (b)11%     (c)12%     (d)22%

Q27. which of the following quantities measured from different inertial reference frames are same ?

(a)force     (b)velocity   (c)displace  (d)kinetic energy

Q28. If the unit of mass, length and time are doubled, unit of angular momentum will be :

(a)doubled   (b)tripled    (c)quadrupled  (d) 8 times the original value

Q29. If E= energy , G gravitational constant,  I = impulse and M = mass, the dimension of GIM2/E2 are same that of

(a)time   (b)mass      (c)length  (d)force

Q30. A new system of unit is evolved in which the values of µ0 and E0 are 2 and 8 respectively. Then the speed of light in this system will be

(a)0.25         (b) 0.5      (c)0.75     (d)1.0

Q31.The velocity of a particle (v) at an instant t is given by ; v=at+bt2 the dimension of b is :

(a)[L]                          (b) [LT-1]

(c)[LT-2]                      (d)[LT-3]

Q32. If the dimensions of a physical quantity are given by MaLbTc,then the physical quantity will be :

(a)velocity if a=1,b=0,c=-1

(b)acceleration if a=1,b=1,c=-2

(c) force if a=0,b=-1,c=–2

(d) pressure if a=1,b=-1,c= -2

Q33.Given that the displacement of an oscillating particle is given by y=Asin (Bx=a+D).The displacement formula for (ABCD)is:

(a)[M0L-1T0]         (b)[M0L0T-1]                                                                      (c)[M0L-1T-1]       (d)[M0LOT0]

Q34. If force (F), work(w) and velocity (v) are taken as fundamental quantities ,then the dimensional formula of time (T)is:

(a)[WFv]                 (b)[WFv-1]                                                                         (c)[W-1F-1v-1]       (d)[WF-1V-1]

Q.35.The potential energy of a particle varies with distance x from a fixed origin as V=(A√x /(x+B)) where A and Bare constant ,The dimensions of AB are:

(a) [ML5/2T-2]         (b)[ML2T-2]                                                                      (c)[ M3/2L3/2T-2]    (d)[ML7/2T-2]

Q36.If force is proportional to square of velocity ,then the dimensions of proportionality constant is:

(a)[ML-1T]                  (b)[ML-1T0]                                                                       (c)[MLT0]                 (d)[M0LT-1]

Q37.The speed (v) of ripples on the surface of water depends on surface tension (σ) ,density density (p) and wavelength (λ) The square of speed (v) is proportional to :

(a) σ/pλ    (b)p/σ λ       (c) λ/ pσ      (d)pσλ

Q38. The modulus of electricity is dimensionally equivalent to :

(a)strain                                      (b)force                  (c)stress                                      (d)coefficient of viscosity

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## assignment electric current class 12

this assignment deals with chapter electric current. this assignment will help the students to practice well and score good marks in board examinations.