introduction to physics H C Verma

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 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 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
  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
  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
  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
  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
  19. Let x and a stand for distance . Is ∫dx/√a2-x2 = 1/a sin-1 a/x . dimensionally correct ? CHECK VIDEO SOLUTION ans – no