1. Which of the following is not the unit of distance? (a) Light year (b) Astronomical Unit (c) Parsec (d) Millisecond
2. The dimensional formula for ω in the relation y = A Sin ωt is (a) [M° L° T] (b) [M° L° T–1] (c) [ML° T°] (d) [M° L–1 T–1]
3. Dimensional formula for curie is (a) [M° L T–1] (b) [M° L–1 T°] (c) [M° L° T–1] (d) [M–1 L° T°]
4. Which of the following pairs of physical quantities does not have same dimensional formula. (a) Work and torque (b) Angular momentum and Planck's constant (c) Tension and surface tension (d) Impulse and linear momentum
5. If momentum (p), Area (A) and time (T) are takes as fundamental quantities, then energy has the dimensional formula : (a) [ p A½ T–1 ] (b) [ p A–½ T1 ] (c) [ p2 A T ] (d) [ p A–1 T ]
6. Out of 4.0 and 4.00, which is more accurate? (a) 4.0 (b) 4.00 (c) Both are equally accurate (d) Nothing can be said
7. The speed (v) of sound in a gas is given by v = k Px ρy Where K is dimensionless constant, P is pressure, and ρ is the density, then (a) x = ½, y = ½ (b) x = –½, y = –½ (c) x = ½, y = –½ (d) x = –½, y = ½
8. If percentage errors in the measurement of mass and volume of an object are 2% and 3% respectively, then the percentage error in the measurement of the density of the object is : (a) 1% (b) 0.66% (c) 5% (d) 6%
9. Given that n -1 2 dx x-a = a sin 2ax-x a ∫ Where a is a constant. Using dimensional analysis the value of n is (a) 1 (b) –1 (c) 0 (d) None of the above
10. In the standard equation nth a S = u + (2n-1) 2 what dimensions do you view for Snth (a) [ M° L1 T°] (b) [ M° L–1 T] (c) [ M° L T–1 ] (d) [ M° L° T1 ]
11. Given force = α density + β3 what are dimensions of α, β ? (a) ML–2 T–2 , ML–1/3 (b) M2 L4 T–2, M1/3 L–1 (c) M2 L–2 T–2, M1/3 L–1 (d) M2 L–2 T–2, M L–3
12. The dimensions of intensity are (a) [ L° M T–3 ] (b) [ L1 M2 T–2 ] (c) [ L2 M T–2 ] (d) [ L2 M2 T–3 ]
13. The dimensions of light year is (a) T (b) L T–1 (c) L (d) T–1
14. The time dependence of a physical quantity P is given by P = Po exp.(–αt 2), where α is a constant and t is time, The constant α is (a) dimensionless (b) has dimensions T–2 (c) has dimensions of P (d) has dimensions T2
15. Two quantities A and B have different dimensions. Which mathematical operation may be physically meaningful. (a) A/B (b) A+B (c) A–B (d) A = B
16. Which one of the following pair of quantities has the same dimension? (a) force and work done (b) momentum and impulse (c) pressure and force (d) surface tension an force
17. A cube has a side of length 1.2×10–2 m. Calculate its volume. (a) 1.7 ×10–6 m3 (b) 1.73 ×10–6 m3 (c) 1.0 ×10–6 m3 (d) 1.732 ×10–6 m3
18. The equation of state for a real gas is given by 2 a P + (v – b) = RT v the dimensions of constant a are (a) [ M L5 T–2 ] (b) [ M–1 L5 T2 ] (c) [ M L–5 T–1 ] (d) [ M L5 T–1 ]
19. The number of significant figures in 30.00 m are (a) 1 (b) 2 (c) 3 (d) 4
20. Which of the following measurements is most precise? (a) 5.00 m (b) 5.00 km (c) 5.00 cm (d) 5.00 mm
Answer Key : 1. (d) 2. (b) 3. (c) 4. (c) 5. (a) 6. (b) 7. (c) 8. (c) 9. (c) 10. (c) 11. (c) 12. (a) 13. (c) 14. (b) 15. (a) 16. (b) 17. (a) 18. (a) 19. (d) 20. (d)
HINTS AND EXPLANATIONS :
2. ωt = Angle = dimensionless so dimension of ω = 1 t = [ M° L° T–1 ]
3. curie = unit of radioactivity = dN Number/dt time = [ T–1] or [M° L° T–1 ]
4. Surface tension and Tension have different dimension Tension = Force = [MLT–2] Surface tension = Force –2 = [M T ] length
5. Energy = Force × Length change in momentum ½ –1 × area [p A A ] time = =
7. v = k Px ρy [M° L T–1] = [M L–1 T–2] x [M L–3] y 0 = x + y , 1 = –x –3y , –1 = –2x y = –x x = ½ = – ½
8. m 100 100 100 2% 3% 5% m ∆ρ ∆ ∆ν × = × +× = + = ρ ν
9. L n = a L No dimension 1 = an Possible for n = 0
11. Dimension of 3 β = dimension of density Solve, 1/3 1 β [ ] M L− = Force = 2 3 22 2 density Force density [M L T M L ] [M L T ] − − − − α α= × = =
12. Intensity = energy area time × 2 2 3 3 2 ML T [M T ] [M L T ]
13. Light year = distance = L
14. α t 2 = constant 2 2 1 [T ] t − α= =
16. Momentum and Impulse have some dimension = [M L T–1]
17. Volume = (side)3 2 3 6 6 3 (1.2 10 ) 1.728 10 1.7 10 m − −− = × = × =×
18. dimension of a = 2 1 26 5 2 PV [M L T L ] [M L T ] − − − = =
20. 5.00 mm is most precise because it have least least count.
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