Units and Dimensions Physics Problems PDF

Units and dimensions 1- Find the dimensions and SI units for the following quantities: 1- Pressure 2- Work 3- Kinetic energy Sol. 2- Check the correctness of the following relation: ]P] = M L-1 T-2 [ = M L-1 T-2 L.H.S. = R.H...

Units and dimensions 1- Find the dimensions and SI units for the following quantities: 1- Pressure 2- Work 3- Kinetic energy Sol. 2- Check the correctness of the following relation: ]P] = M L-1 T-2 [ = M L-1 T-2 L.H.S. = R.H.S. The equation is correct. 3- Derive an equation for the speed of sound in a gas of density ρ and pressure P where constant K=Π.  Sol. =Π ] [ =Π [] [ L =. L =.. y= & x= ⁄ ⁄ =Π Or = Π√ 4- A sphere of radius r is moving through a fluid of density ρ with velocity v experiences a retarding force F giving by "Where K is a dimensionless constant." Find x, y and z. Sol. ]F[ =  y=1 , z=2 & x=2 5- Find the dimensions and units of the potential energy. Sol. [P.E] = [m] [g] [h] = M (LT-2) L = M L2 T-2 Units → Kg.m2.s-2 =Joule 6- Check the correctness of the following equation: P=ρgh Sol. L.H.S. = ]P[ = ML-1 T-2 R.H.S. = ]ρ[ ]g[ ]h[ = ML-3.LT-2.L =M L.H.S. = R.H.S. The equation is correct. 7- Convert the unit of Energy from Joule (M.K.S) system to erg )c.g.s( system. Sol. Joule = kg.. erg = g.. J= = = = g.. = erg 8- Convert the unit of Force from Newton (M.K.S) system to Dyne)c.g.s( system. Sol. Dimensions → [F] = M L T-2 Units → 1 N = = 1 N = 105 Dyne 9- Force of viscosity "F" acting on a spherical body moving through a fluid depends on its velocity"v", radius "r" and co-efficient of viscosity "η" of the fluid through the relation F=6Пηvr  Find the dimensions of "η". Sol. F=6Пηvr [M L T-2] = η [L T-1] [L] Where the constant "6П" has no dimensions. →η= [ ] 10- Find units and dimensions of "Young modulus" Y= Sol. [ ] Dimensions → [Y] = = M L-1 T-2 [ ] Units → Kg.m-1.s-2 = N/m2 11: Find the dimensions and SI units for the following quantities: 1-Area 2- Volume 3- Velocity 4- Density 5- Acceleration 6- Force 7- Frequency 8- Momentum 12: Find the correct relation: 13: Check the correctness of the following relation:  √ 14: Check the correctness of the following relation: ⁄ 15: The period of a simple pendulum (T) is assumed to depend on length (L) of pendulum, acceleration due to gravity (g) and mass (m) of the bob of the pendulum. If the constant of proportionality is (2ᴫ), then find the equation for time period of the simple pendulum. 16: The centrifugal force (F) acting on a body depends on the mass (m) of the body, its linear velocity (v) and radius of the circular path (r). Find the value of (F). 17: Find the dimensions of energy from the following relations: K.E = E = m c2 18: Convert the unit of Pressure from Pascal (M.K.S) system to Bar)c.g.s( system. 19: Find the dimensions of Planck's constant from the equation: E=hʋ 20: Find units and dimensions of "Bulk modulus" Y= =