Units and Measurements-Quiz-4

UNITS AND MEASUREMENTS QUIZ-4

Dear Readers,

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts.

Q1. 

•  0
•  2
•  -2
•  1

Solution

(b)
Here xⁿ has the same dimensions as a² . Thus n=2 will make the expression dimensionally correct

Q2. A physical quantity depends upon five factors, all of which have dimensions; then method of dimensional analysis

•  Can be applied
•  Cannot be applied
•  Depends upon factors involved
•  Both a and c

Solution

(b)
If a quantity depends upon more than three factors, each having dimensions, then the method of dimensional analysis cannot be applied. It is because applying principle of homogeneity will give only three equations

Q3. 

•  7 %
•  9 %
•  11 %
•  9.5 %

Solution

Q4. 

•  M L T
•  M L T⁰
•  M L⁰ T⁰
•  M⁰ L⁰ T⁰

Solution

Q5. The relative density of a material of a body is found by weighing in first in air and then in water. If the weight of the body in air is W₁=8.00 ± 0.05 N and weight in water is W₂=6.00 ± 0.05 N, then the relative density ρ_r=W₁/(W₁-W₂) with the maximum permissible error is

•  4.00 ± 0.62 %
•  4.00 ± 0.82 %
•  4.00 ± 3.2 %
•  4.00 ± 5.62 %

Solution

Q6. 

•  Due to the errors in the measurements of d and l are the same
•  Due to the error in the measurement of d is twice that due to the error in the measurement of l
•  Due to the error in the measurement of d is twice that due to the error in the measurement of l
•  Due to the error in the measurement of d is four time that due to the error in the measurement of l

Solution

Q7. If C, the velocity of light, g, the acceleration due to gravity, and P, the atmospheric pressure are the fundamental quantities in M.K.S. system, then the dimensions of length will be same as that of

•  C / g
•  C / P
•  P C g
•  C²/g

Solution

Q8. The relation tan⁡θ=v²/rg gives the angle of banking of the cyclist going round the curve. Here v is the speed of the cyclist, r is the radius of the curve, and g is acceleration due to gravity. Which of the following statements about the relation is true?

•  It is both dimensionally as well as numerically correctt
•  It is neither dimensionally correct nor numerically correct
•  It is dimensionally correct but not numerically
•  It is numerically correct but not dimensionally

Solution

Q9. A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mm and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is

•  1
•  2
•  3
•  4

Solution

Q10. A physical quantity x depends on quantities y and z as follows: x = A y + B tan⁡(Cz), where A,B and C are constants. Which of the following do not have the same dimensions?

•  x and B
•  C and z^-1
•  y and B / A
•  x and A

Solution