EXERCISES & SOLUTIONS TO CONCEPTS OF PHYSICS H.C. VERMA BOOK
1. Find the dimensions of (a) linear momentum, b) frequency and (c) pressure.
1. a) Linear momentum : mv = [MLT–1] b) Frequency : T 1 = [M0 L0 T–1] c) Pressure : L[ ] [MLT ] Area Force 2 2 = [ML–1T–2]
2. Find the dimensions of (a) angular speed ω, (b) angular acceleration α, (c) torque Γ and (d) moment of interia I. Some of the equations involving these quantities are Introduction to Physics 9ω = θ2 − θ1 t2 − t1 , α = ω2 − ω1 t2 − t1 , Γ = F.r and I = mr 2 . The symbols have standard meanings.
2. a) Angular speed = /t = [M0 L0 T–1] b) Angular acceleration = T M L T t 0 0 2 [M0 L0 T–2] c) Torque = F r = [MLT–2] [L] = [ML2 T–2] d) Moment of inertia = Mr2 = [M] [L2 ] = [ML2 T0 ]
3. Find the dimensions of (a) electric field E, (b) magnetic field B and (c) magnetic permeability µ 0. The relevant equations are F = qE, F = qvB, and B = µ 0 I 2 π a ; where F is force, q is charge, v is speed, I is current, and a is distance.
3. a) Electric field E = F/q = [MLT I ] [IT] MLT 3 1 2 b) Magnetic field B = [MT I ] [IT][LT ] MLT qv F 2 1 1 2 c) Magnetic permeability 0 = [MLT I ]
4. Find the dimensions of (a) electric dipole moment p and (b) magnetic dipole moment M. The defining equations are p = q.d and M = IA; where d is distance, A is area, q is charge and I is current.
4. a) Electric dipole moment P = qI = [IT] × [L] = [LTI] b) Magnetic dipole moment M = IA = [I] [L2 ] [L2 I]
5. Find the dimensions of Planck’s constant h from the equation E = hν where E is the energy and ν is the frequency.
5. E = h where E = energy and = frequency. h = [ML T ]
FORE MORE ANSWERS COMEENT IN COMMENT BOX I WILL UPLOAD THE ANSWERS....
6. Find the dimensions of (a) the specific heat capacity c, (b) the coefficient of linear expansion α and (c) the gas constant R. Some of the equations involving these quantities are Q = mc(T2 − T1), lt = l0[1 + α(T2 − T1)] and PV = nRT.
7. Taking force, length and time to be the fundamental quantities find the dimensions of (a) density, (b) pressure, (c) momentum and (d) energy.
8. Suppose the acceleration due to gravity at a place is 10 m/s 2. Find its value in cm/(minute) 2 .
9. The average speed of a snail is 0. 020 miles/hour and that of a leopard is 70 miles/hour. Convert these speeds in SI units.
10. The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = 13. 6, Density of water = 103 kg/m3 , g = 9. 8 m/s2 at Calcutta. Pressure = hρg in usual symbols.
11. Express the power of a 100 watt bulb in CGS unit.
12. The normal duration of I.Sc. Physics practical period in Indian colleges is 100 minutes. Express this period in microcenturies. 1 microcentury = 10 – 6 × 100 years. How many microcenturies did you sleep yesterday ?
13. The surface tension of water is 72 dyne/cm. Convert it in SI unit.
14. The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speed ω. Assuming the relation to be K = kI a ω b where k is a dimensionless constant, find a and b. Moment of inertia of a sphere about its diameter is 2 5 Mr 2 .
15. Theory of relativity 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.
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. Dimensional formulae for R and V are ML2 I − 2 T− 3 and ML2 T− 3 I − 1 respectively.
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.
18. Test if the following equations are dimensionally correct : (a) h = 2 S cosθ ρrg , (b) v = √ P ρ , (c) V = π P r 4 t 8 η l , (d) ν = 1 2 π √mgl I ; where h = height, S = surface tension, ρ = density, P = pressure, V = volume, η = coefficient of viscosity, ν = frequency and I = moment of inertia.
19. Let x and a stand for distance. Is ∫ dx √ a 2 − x 2 = 1 a sin− 1 a x dimensionally correct
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