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 : $MLT^{-1}$ $ML^{2}T^{-2}$ $ML^{-1}T^{-2}$ $ML^{2}T^{-1}$ 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 $FA^{2}V^{-2}$ $FA^{2}V^{-3}$ $FA^{2}V^{-4}$ $FA^{2}V^{-5}$ 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 $M^{0}LT^{2}$ $M^{0}L^{2}T^{-4}$ $M^{0}LT^{-3}$ $M^{0}L^{2}T^{-1}$ 4. If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be : $FT^{2}$ $F^{-1}A^{2}T^{-1}$ $FA^{2}T$ $AT^{2}$ 5. The unit of Stefan-Boltzmann’s constant ($\alpha $) is 6. Which of the following is not equal to watt ? $joule/second$ $ampere\times volt$ $ \left ( ampere \right )^{2}\times ohm$ $ampere/volt$ 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 $\gamma$. $LT^{-1}$ $T^{-1}$ $T^{-2}$ $\frac{T^{-1}}{L}$ 8. One kilowatt-hour is equal to : $3.6\times 10^{6}joule$ $3.6\times 10^{5}joule$ $10^{3}joule$ $10^{7}joule$ 9. The value of G is $6.67\times 10^{11}$ in MKS unit, its value in CGS unit is : $6.67\times 10^{-10}$ $6.67\times 10^{-8}$ $6.67\times 10^{-5}$ $6.67\times 10^{-7}$ 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 $M^{0}L^{0}T^{0}$ $M^{0}L^{-1}T^{0}$ $M^{0}L^{0}T^{-1}$ $M^{0}LT^{-1}$ 11. Which of the following measurements is most accurate ? 0.005 mm 5.00 mm 50.00 mm 5.0 mm 12. When 97.52 is divided by 2.54, the correct result is $38.3937$ $38.394$ $38.39$ $38.4$ 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 n = 10, m = 0.5 cm n = 9, m = 0.4 cm n = 10, m = 0.8 cm n = 10 , m = 0.2 cm 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? 1 N Infinity N/2 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 $W$ $l$ $r$ $\theta$ 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 0.1% 8% 1.8% 0.8% 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 (αa – βb + γc)% (αa + βb + γc)% (αa – βb – γc)% none of the above 18. The measure of radius of a sphere is (4.22 ± 2%) cm. The percentage error in volume of the sphere is (315 ± 6%) (315 ± 2%) (315 ± 4%) (315 ± 5%) 19. The percentage error in measurement of a physical quantity m given by $m=\pi tan\theta $ is minimum when $\theta = 45^{o}$ $\theta = 90^{o}$ $\theta = 60^{o}$ $\theta = 30^{o}$ 20. When the number 6.03587 is rounded off up to the second place of decimals, it becomes 6.035 6.04 6.03 none of these 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) 0.85 m/s 0.9 m/s 1.0 m/s 0.8 m/ 22. The number of significant figures in 0.00040 m is 1 2 3 4 23. No of significant digits in 720 and 510m is 3 and 3 3 and 2 2 and 3 2 and 2 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) 1.8 /(N) 1.8 /(N+2) 1.8 /(N-2) none 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. $9\left (\alpha _{1}- \alpha _{2} \right )\Delta T$ $9\left (\alpha _{1}+ \alpha _{2} \right )\Delta T$ $\frac{1}{9}\left (\alpha _{1}+ \alpha _{2} \right )\Delta T$ $\frac{1}{9}\left (\alpha _{1}- \alpha _{2} \right )\Delta T$ Loading … Question 1 of 25