## Units And Dimensions Quiz-9

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. Write dimensional formula for the intensity of radiation
•  M1L0 T3
•  M1L0 T-3
•  M1L2 T-2
•  M1L2 T-3
Solution

Q2.Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful
•  A/B
•  A+B
•  A-B
•  None of these
Solution
(a) Quantities having different dimensions can only be divided or multiplied but they cannot be added or subtracted

Q3.   The percentage errors in the measurement of a mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed?
•  11 %
•  8 %
•  5 %
•  1 %
Solution
(b) We know that kinetic energy =1/2 mv2 Required percentage error is 2%+2×3% ie,8%

Q4. The concordeis the fastest airlines used for commercial service. It can cruise at 1450 mile per hour (about two times the speed of sound or in other words mach 2). What is it in m/s?
•  644.4m/s
•  80 m/s
•  40 m/s
•  None of These
Solution
(a) n1 u1=n2 u2 n2=(n1 u1)/u2 =(1450mile/h)/(m/s)=(1450 s/mile)/mh =(1450 s×1.6km)/(〖10〗^(-3) km 60×60s)=644.4 1450 mile/h=644.4m/s

Q5.The dimensions of electric potential are
•  [ML2T-2Q-1]
•  [ML1T-2Q-1]
•  [ML2T-1Q1]
•  [ML2T-2Q1]
Solution
(a) V=W/Q=[ML2T-2Q-1]

Q6. The internal and external diameters of a hollow cylinder are measured with the help of a vernier calipers. Their values are 4.23 ± 0.01 cm and 3.87 ± 0.01 cm respectively. The thickness of the wall of the cylinder is
•  0.36± 0.02 cm
•  0.18± 0.02 cm
• 0.36± 0.01 cm
•  0.18± 0.01 cm
Solution
(b) Subtract 3.87 from 4.23 and then divide by 2.

Q7.The velocity v (in cm/sec) of a particle is given in terms of time t(in sec) by the relation v=at+b/(t+c) ; the dimensions of a,b and c are
•  a=L2,b=T,c=LT2
•  a=LT2,b=LT,c=L
•  a=LT2,b=L,c=T
•  a=L,b=LT,c=T2
Solution
(c) From the principle of dimensional homogenity [v]=[at]⇒[a]=[LT-2)]. Similarly [b]=[L] and [c]=[T]

Q8.The dimensions of kinetic energy are
•  [M2 L2 T]
•  [M1 L2T]
•  [M1 L2T-2]
•  [M1 L2 T-1]
Solution
(c) KE=1/2 mv2 ∴[KE]=[M] [LT-1]2=[ML2 T-2 ]

Q9 .What is the SI unit of permeability
•  Henry per meter
•  Tesla meter per ampere
•  Weber per ampere meter
•  All of the above units are correct
Solution
(d)

Q10. A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is
•  e2-e1
•  e1+2e2
•  e1+e2
• e1-2e2
Solution
(b) In g=ln⁡〖h-2 ln ⁡t 〗 (∆g/g×100)max=∆h/h×100+2∆t/t×100=e1+2e2

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