### UNITS, DIMENSIONS & ERROR ANALYSIS TEST 2

1. The dimension of  $\left ( \frac{1}{2} \right )\varepsilon _{o}E^{2}$ ($\varepsilon _{o}$ : permittivity of free space; E: electric field ) is :

2. If the velocity (V), acceleration (A) and force (F) are taken as fundamental quantities instead of mass (M), length (L) and time (T), the dimension of Young’s modulus would be

3. The number of particles crossing per unit area perpendicular to X – axis in unit time is $N=-D\frac{n_{2}-n_{1}}{x_{2}-x_{1}}$

where $n_{1}$ and $n_{2}$ are number of particles per unit volume for the value of $x_{1}$ and $x_{2}$ respectively. The dimensions of diffusion constant D are

4. If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be :

5. The unit of Stefan-Boltzmann’s constant ($\alpha$) is

6. Which of the following is not equal to watt ?

7. Viscous force F is given by $F=\eta A\gamma$ where $\eta$ and A are the coefficient of viscosity and area respectively. The dimensional formula for $\gamma$.

8. One kilowatt-hour is equal to :

9. The value of G is $6.67\times 10^{11}$ in MKS unit, its value in CGS unit is :

10. The force acting on a body is represented as $F=A cosBx+C sinDt$ ,where $x$ is displacement and $t$ is time. The dimensions of $\frac{D}{B}$ are

11. Which of the following measurements is most accurate ?

12. When 97.52 is divided by 2.54, the correct result is

13. A vernier callipers having 1 main scale division = 0.1 cm is designed to have a least count of 0.02 cm. If n be the number of divisions on vernier scale and m be the length of vernier scale, then

14. In a Vernier Calipers (VC), N divisions of the main scale coincide with N + m divisions of the vernier scale. What is the value of m for which the instrument has minimum least count?

15. In the measurement of n from the formula  $n=\frac{2Wgl}{\pi r^{4}\theta }$  the quantity which should be measured with best care is

16. The least count of a stopwatch is 1/5 second. The time for 20 oscillations of a pendulum is measured to be 25 seconds. The percentage error in the measurement of time will be

17. A physical quantity is represented by $X=M^{a}L^{b}T^{-c}$ . If percentage error in the measurement of M, L and T are α%, β% and γ%  respectively, then total percentage error is

18. The measure of radius of a sphere is (4.22 ± 2%) cm. The percentage error in volume of the sphere is

19. The percentage error in measurement of a physical quantity m given by $m=\pi tan\theta$ is minimum when

20. When the number 6.03587 is rounded off up to the second place of decimals, it becomes

21. A body is moving from height x = 0.1 m to x = 1.2 m in 1 sec under constant acceleration of $0.5 m/s^{2}$. What was the initial velocity with which it started. (Correct to significant digits)

22. The number of significant figures in 0.00040 m is

23. No of significant digits in 720 and 510m is

24. In a vernier calipers the main scale and the vernier scale are made up different materials. When the room temperature increases by $\Delta T^{o}C$, it is found the reading of the instrument remains the same.Earlier it was observed that the front edge of the wooden rod placed for measurement crossed the $N^{th}$ main scale division and N + 2 msd coincided with the $2^{nd}$ vsd. Initially, 10 vsd coincided with 9 msd. If coefficient of linear expansion of the main scale is $\alpha _{1}$  and that of the vernier scale is $\alpha _{2}$  then what is the value of  $\alpha _{1}$ / $\alpha _{2}$ ? (Ignore the expansion of the rod on heating)

25. Consider the MB shown in the diagram, let the resistance X have temperature coefficient $\alpha _{1}$ and the resistance from the RB have the temperature coefficient $\alpha _{1}$ . Let the reading of the meter scale be 10cm from the LHS. If the temperature of the two resistance increase by small temperature $\Delta T$ then what is the shift in the position of the null point? Neglect all the other changes in the bridge due to temperature rise.

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