introduction to physics H C Verma

The Introduction chapter of H.C. Verma’s Concepts of Physics explains the basic idea of physics and its role in understanding nature. It introduces physics as the study of matter, energy, motion, forces, space, and time.

The chapter briefly discusses:

  • The scope and importance of physics
  • Discuss about different types of unit
  • Discuss about dimension and its uses
  • Discuss about order of magnitude and significant figure
  • Physical laws and theories
  • The role of experiments and observations
  • Mathematical methods used to describe physical phenomena
  • How physics helps us understand everyday natural events and technology

OBJECTIVE 1

1)Which of the following sets cannot enter into the list of fundamental quantities in any system of units ? A length, mass and velocity B length, time and velocity C mass, time and velocity D length, time and mass CHECK VIDEO SOLUTION

ans– B) length ,time , velocity

2)A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then a-  n ∝ size of u    b n∝u2    c n∝√u     d n∝1/u CHECK VIDEO SOLUTION

ans- D) n∝1/u

3)Suppose a quantilty x can be dimensionally represented in terms of M,L and T, that is x, MaLbT c. The quantity mass a) can always be dimensionally represented in terms of  L , T and  X b)  can never be dimensionally represented in terms of  L T and X c) may be represented in terms of  L T and  x  if a= 0  d) may be represented in terms of  L,T and X   if  a≠ 0 CHECK VIDEO SOLUTION

ans – d) may be represented in terms of  L,T and X   if  a≠ 0

4) A dimensionless quantity A Must not have a unit B May have a unit C May not have a unit D Must have a unit CHECK VIDEO SOLUTION

ans – B May have a unit

5) A unitless quantity A never has a nonzero dimension B always has a nonzero dimension C may have a nonzero dimension. D  does not exist CHECK VIDEO SOLUTION

ans – A never has a nonzero dimension

6) In the equation ∫dx/√2ax- x2 . Find the value of n is  .a) 0 b) -1 c) 1 d) none of these CHECK VIDEO SOLUTION

ans – a) 0

OBJECTIVE 2

1) The dimensions of   ML-1T-2 may correspond to a) workdone by force b)linear momentum c)pressure d)energy per unit volume

CHECK VIDEO SOLUTION

ans – c and d

2) Choose the correct statement(s). A dimensionally correct equation must be correct. B dimensionally correct equation may be in correct. C A dimensionally incorrect equation must be correct. D A dimensionally incorrect equation may be correct CHECK VIDEO SOLUTION

ans- a,b,d

3) Choose the correct statement(s)… A All quantities may be represented dimensionally in terms of the base quantities B A base quantity cannot be represented dimensionally in terms of the rest of the base quantities C The dimension of a base quantity in other base quantities is always zero.D The dimension of a derived quantity is never zero in any base quantity. CHECK VIDEO SOLUTION

ans – a,b,c

EXERCISES

  1. Find the dimensions of a)linear momentum b) frequency c) pressure CHECK VIDEO SOLUTION ans– a) MLT-1 b) T-1 c)M1L-1T-2
  2. Find the dimension of a) angular speed b) angular acceleration c) torque d) moment of inertia CHECK VIDEO SOLUTION ans-a)T-1 b)T-2 c) ML2T-2 d) ML2
  3. Find the dimension of a) electric field E b) magnetic field B c) magnetic permeability μ° CHECK VIDEO SOLUTION ans a- MLT-3A-1 b) MT-2A-1 c)MLT-2A-2
  4. Find the dimension of a) electric dipole moment b) magnetic dipole moment CHECK VIDEO SOLUTION ans a- ATL b)L2A
  5. Find the dimension of planck’s constant h from the equation E = hυ where E is energy , υ is the frequency . CHECK VIDEO SOLUTION ans ML2T-1
  6. Find the dimension of a)the specific heat capacity b) the coefficient of linear expansion c) the gas constant CHECK VIDEO SOLUTION ans a)L2T-2K-1 b)K-1 c)ML2T-2K-1 (mol)-1
  7. Taking force, length and time to be fundamental quantities find the dimension of a)density b)pressure c)momentum d) energy CHECK VIDEO SOLUTION ans a)FL-4T2 b)FL-2 c)FT d)FL
  8. Suppose the acceleration due to gravity at a place is 10m/s2 . find its value in cm/minute2 . CHECK VIDEO SOLUTION ans 36*10 5 cm/min 2
  9. The average speed of a snail is 0.20 miles/hour and that of leopard is 70 miles/hour . convert these speed in SI unit . CHECK VIDEO SOLUTION ans 0.0089m/s , 31m/s
  10. The height of mercury column in a barometer in Calcutta labrotory was recorded to be 75cm . calculate this pressure in si and cgs unit using following data : CHECK VIDEO SOLUTION ans 10 * 10 4 N/M2 , 10 *105 dyne/cm2
  11. Express the power of a 100 watt bulb in CGS unit . CHECK VIDEO SOLUTION ans 10 9 erg/s
  12. The normal duration of I SC physics practical period in indian colleges is 100 min . Express this period in microcenturies . I microcentury = 10-6 * 100 years . How many microcenturies did you sleep yesterday ? CHECK VIDEO SOLUTION ans 1.9 microcentury
  13. The surface tension of water is 72 dyne/cm . convert it in SI unit ? CHECK VIDEO SOLUTION ans 0.072 N/M
  14. The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speed . Assuming the relation to be  K= k IaWb , where k is a dimensionless constatnt, find a and b. Moment of inertia of a spere about its diameter is 2/5Mr2. CHECK VIDEO SOLUTION ans a=1 b=2 Ans :  K ∝ IaWb K = constant  I a W b LHS = K = ½ mv2 = M(LT-1)2= M1L2T-2 RHS = (ML2)a(T b= Ma L2aT-b Equating LHS and RHS a= 1  2a= 2 , a=1 b=2 K = constant . I1 W2
  15.  Theory of reltivity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a relation among the quantities using the method of dimensions. CHECK VIDEO SOLUTION ans E= kmc2 Ans : E ∝ Ma C b , E = constant . Ma Cb , LHS E= M1L2T-2 RHS  constant . MaCb , Ma (L1T-1)b, Ma LbT-b , equating LHS and RHS a= 1 b=2 so E= constant M1 C2
  16. Let I= current through a conductor, R= its resistance and V= potential difference across its ends. According to Ohm’s law, product of two of these quantities equals the third. Obtain Ohm’s law from dimensional analysis. Dimensonal formulae for R andV are  ML2T-3I-2 and ML2T-3I-1  respectively. CHECK VIDEO SOLUTION ans V=IR Ans V =  iR LHS V =ML2T-3A-1 RHS iR = A M1L2T-3A-2 = ML2T-3A-1
  17. The frequency of vibration of a string depends on the length L between the nodes, the tension F in the string and its mass per unit length m . Guess the expression for its frequency from dimensional analysis . CHECK VIDEO SOLUTION ans – k/L √F/M ANS : f ∝ L a F b  m C , f = constant L a F b m c ,  LHS = f= T-1 RHS  La Fb mc = La (MLT-2)b (ML-1)c = Mb+c La+b-c T-2b equating LHS and RHS  T-2b = T-1 ,b= ½ Mb+c = M0 , b+c = 0 , ½+c = 0 , c= -1/2  La+b-c = L0 , a+b-c= 0 , a+1/2-(-1/2)= 0 ,a=1 Hence f= constant L1F1/2m-1/2    
  18. Test if the following equations are dimensionally correct a) h= 2scosθ/ρrg b)υ=√p/ρ   c) V = πpr4t/8ηl     d)υ=1/2π √mgl/I CHECK VIDEO SOLUTION ans all are dimensionally correct

Ans) A LHS h = [L] RHS 2scosθ/ρrg = MT-2/ ML-3 L LT-2 = L

B LHS υ= LT-1 RHS √p/ρ = √ML-1T-2/ML-3 = √L2T-2 = LT-1

C LHS V= L3/T-1 RHS πpr4t/8ηl = πpr4t/8ηl = ML-1T-2 L4 T / ML-1T-1.L = L3T-1

D LHS υ= T-1 RHS 1/2π √mgl/I = 1/2π √mgl/I =  √MLT-2/ML2 = √T-2 = T-1

19) Let x and a stand for distance . Is ∫dx/√a2-x2 = 1/a sin-1 a/x . dimensionally correct ? CHECK VIDEO SOLUTION

Ans ) LHS = ∫dx/√a2-x2 = L/√L2= L/L = M0L0T0 RHS = 1/L= L-1 LHS ≠ RHS it is not dimensionally correct .