## Basic Maths, Vectors,Units and Dimensions Quiz-8

As per analysis for previous years, it has been observed that students preparing for NEET find Physics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Biology due to their medical background.

Furthermore, sections such as Physics are dominantly based on theories, laws, numerical in comparison to a section of Biology which is more of fact-based, life sciences, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

Q1. The dimensional formula of 1/Îµ0 e2/hc is
•  [M0L0T0A0]
•  [M-1L3T2A]
•  [ML3T-4 A-2
•  [M-1L-3T4
Solution
(a) The formula for fine structure constant is =e2/(4Ï€Îµ0(h/2Ï€)c)

Q2.In the formula, a=3bc2,a and c have dimensions of electric capacitance and magnetic induction respectively. What are dimensions of b in MKS system?
•  [M-3L-2T4 Q4]
•  [M-3T4 Q4]
•  [M-3T3Q]
•  [M-3L2T4Q-4]
Solution
(a) Given, a=3bc2 ⟹ b=a/(3c2) Writing dimensions for a and c, we have [b]=[Q/V]/[B]2=([Q][ML2T-2Q-1])/[MT-1Q-1]2 =[M-3L-2T4Q4]

Q3.  A unit of area, often used in measuring land areas, is the hectare defined as 104m2. An open-pit coal mine consumes 75 hectares of land, down to a depth of 26m, each year. What volume of earth, in cubic kilometre, is removed in this time
•  0.01
•  0.02
•  0.03
•  0.04
Solution
(b) Required volume =(75×104×26)/(103×〖103×103) (km)3

Q4. If 3.8 ×10-6is added to 4.2 ×10-5 giving due regard to significant figures, then the result will be
•  458×10-5
•  4.6×10-5
•  4.5x10-5
•  None of these
Solution
(b)

Q5.Let us choose a new unit of length such that the velocity of light in vacuum is unity. If light takes 8 min and 20 sec to cover the distance between sun and earth, this distance in terms of the new unit is
•  5
•  50
•  500
•  3x108
Solution
(c) New unit of distance = speed in new units × 500 s

Q6. If L,C and R denote inductance, capacitance and resistance respectively, then which of the following combination has the dimension of time?
•  C/L
•  1/RC
• L/R
•  RL/C
Solution
(c) Dimensions of L and R [R]=[ML2T-3A-2] [L]=[ML2T-2) A-2] [L/R]=[ML2T-2A-2]/[ML2T-3A-2] =[T]

Q7.In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (=0.5°) then the least count of the instrument is
•  one minute
•  Half minute
•  One degree
•  Half degree
Solution
(a) 30 VSD=29 MSD 1 VSD=29/30 MSD L.C.=1 MSD-1 VSD = (1-29/30) MSD=1/30×0.5°=1 minute

Q8.The position of a particle at time t is given by the relation x(t)=((v0/Î±))(1-eÎ±t), where v0 is constant and Î±>0. The dimensions of v0 and Î± are respectively
•  M0L1T-1and T-1
•  TM0L1T0and T-1
•  M0L1T-1and LT-2
•  M0L1T-1and T
Solution
(a) Dimension of Î±t=[M0L0T0]∴[Î±]=[T-1] Again [v0/Î±]=[L] so [v0]=[LT-1]

Q9.Out of the following which pair of quantities do not have same dimensions
•  Planck’s constant and angular momentum
•  Work and Energy
•  Pressure and Young’s modulus
•  Torque and moment of inertia
Solution
(d) Torque = [ML2T-2], Moment of inertia [ML2]

Q10. The unit of physical quantity obtained by the line intergral of electric field is
•  NC-1
•  Vm-1
•  JC-1
• C2N-1m-2
Solution
(c) The unit of physical quantity obtained by the line intergral of electric field is JC-1.

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