UNITS, DIMENSIONS & ERROR ANALYSIS TEST 3 1. If $x=at+bt^{2}$ , where x is in metres and t is in hours, the unit of b will be 2. The equation of the stationary wave is $y=2Asin\left ( \frac{2\pi ct}{\lambda } \right )cos\left ( \frac{2\pi x}{\lambda } \right )$. Which of the following statements is wrong ? The unit of ct is same as that of λ The unit of x is same as that of λ The unit of 2πc/λ is same as that of 2πx/λt The unit of c / λ is same as that of x / λ 3. Volume of liquid flowing per second through a capillary tube V is given by $V=\frac{K\left ( x_{2}-x_{1} \right )^{4}}{\left ( y_{2}-y_{1} \right )}$ , where $x_{1}$ and $x_{2}$ are inner and outer radii and $y_{2}$ and $y_{1}$ are the positions crossed by the liquid. The dimensional formula for K is : 4. If V denotes the potential difference across the plates of a capacitor of capacitance C, the dimensions of $CV^{2}$ is same as that of Time power current work 5. In a system of units in which the unit of mass is a kg, unit of length is b metre and the unit of time is c second, the magnitude of a calorie is 6. If P represents radiation pressure, C represents speed of light and Q represents radiation energy striking a unit area per second, then the non-zero integers, x,y, and z, such that $P^{x}Q^{y}C^{z}$ is dimensionless are x = 1,y = 1,z = 1 x = 1,y = -1,z = 1 x = -1,y = 1,z = 1 x = 1,y = 1,z = 1 7. If the energy (E), velocity (v) and force (F) be taken as fundamental quantity, then the dimension of mass will be : $Fv^{-2}$ $Fv^{-1}$ $Ev^{-2}$ $Ev^{2}$ 8. If L denotes the inductance of an inductor through which a current i is flowing, the dimensions of $LI^{2}$ are 9. The time dependence of a physical quantity P is given by $P=P_{0}e^{-\alpha t^{2}}$ ,where α is a constant and t is time.The constant $\alpha$ is 10. Which of the following is dimensionally correct ? Pressure = energy per unit area Pressure = energy per unit volume Pressure = force per unit volume Pressure = momentum per unit volume per unit time 11. The volume V of water passing any point of a uniform tube during t seconds is related to the cross-sectional area A of the tube and velocity u of water by the relation $V\propto A^{\alpha }u^{\beta }t^{\gamma }$ . Which one of the following will be true ? α = β = γ α ≠ β = γ α = β ≠ γ α ≠ β ≠ γ 12. Which of the following is the most accurate measurement ? 13. The number of significant figures in 600 m is 1 2 3 4 14. The number of significant figures in 0.900 is 1 2 3 4 15. What will be the value of 9.4450 after rounding off to three significant digits ? 9.45 9.44 9.55 None of these 16. What will be the value of 15.7500 after rounding off to three significant digits ? 15.8 15.7 15.6 None of these 17. When 9.535 is rounded off to give three significant figures, then it is equal to 9.53 9.52 9.54 9.5250 18. When 9.525 is rounded off to give three significant figures, then it is equal to 9.53 9.52 10 9.5250 19. The number 3498 rounded off to two significant figures is 20. When 999 mm is added to 100 m, we get 101 m 100.999 m 100.99 m 100.9 m 21. The value of 0.99 – 0.989 is 22. In an experiment, the value of refractive index of glass was found to be 1.54, 1.53, 1.44, 1.54, 1.56 and 1.45 and 1.45 in successive measurements. The mean absolute error is 0.02 0.025 0.03 0.04 23. In Q. 22, the relative error is 0.02 0.025 0.03 0.04 24. In Q. 22, the percentage error is 2 3 5 5 25. The number of significant figures in (i) 10.85 metre (ii) 0.0001234 kg is (i) 4 (ii) 4 (i) 3 (ii) 7 (i) 4 (ii) 7 (i) 2 (ii) 7 Loading … Question 1 of 25