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 ?

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. If the energy (E), velocity (v) and force (F) be taken as fundamental quantity, then the dimension of mass will be :

 
 
 
 

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 ?

 
 
 
 

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 ?

 
 
 
 

12. Which of the following is the most accurate measurement ?

 
 
 
 

13. The number of significant figures in 600 m is

 
 
 
 

14. The number of significant figures in 0.900 is

 
 
 
 

15. What will be the value of 9.4450 after rounding off to three significant digits ?

 
 
 
 

16. What will be the value of 15.7500 after rounding off to three significant digits ?

 
 
 
 

17. When 9.535 is rounded off to give three significant figures, then it is equal to

 
 
 
 

18. When 9.525 is rounded off to give three significant figures, then it is equal to

 
 
 
 

19. The number 3498 rounded off to two significant figures is

 
 
 
 

20. When 999 mm is added to 100 m, we get

 
 
 
 

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

 
 
 
 

23. In Q. 22, the relative error is

 
 
 
 

24. In Q. 22, the percentage error is

 
 
 
 

25. The number of significant figures in (i) 10.85 metre (ii) 0.0001234 kg is

 
 
 
 

Question 1 of 25