Units and Measurements-Quiz-1

UNITS AND MEASUREMENTS QUIZ - 1

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. The length of a strip measured with a metre rod is 10.0 cm. Its width measured with a vernier callipers is 1.00 cm. The least count of the metre rod is 0.1 cm and that of vernier callipers is 0.01 cm. What will be the error in its area?

•  ± 0.01 cm²
•  ± 0.1 cm²
•  ± 0.11 cm²
•  ± 0.2 cm²

Solution

Q2. The frequency f of vibrations of a mass m suspended from a spring of spring constant k is given by f = C m^x k^y, where C is a dimensionless constant. The values of x and y are, respectively

•  1/2 , 1/2
•  -1/2 , -1/2
•  1/2 , -1/2
•  -1/2 , 1/2

Solution

Q3. Which of the following quantities has its unit as newton - second?

•  Energy
•  Torque
•  Momentum
•  Angular momentum

Solution
(c)
Momentum = Force × Time = N s

Q4. Which of the following number has least number of significant figures?

•  0.80760
•  0.80200
•  0.08076
•  80.267

Solution
(c)
0.08076 has least number of significant figures, i.e., 4

Q5. The order of magnitude of 499 is 2, then the order of magnitude of 501 will be

•  4
•  2
•  1
•  3

Solution
(d)
501=0.501×10^3⇒ order of magnitude of 501 is 3

Q6. A physical quantity X is represented by X=(M^x L^-y T^-z). The maximum percentage errors in the measurement of M, L and T, respectively, are a%, b% and c%. The maximum percentage error in the measurement of X will be

•  (ax + by - cz) %
•  (ax - by - cz) %
•  (ax + by + cz) %
•  (ax - by + cz) %

Solution

Q7. The effective length of a simple pendulum is the sum of the following three: Length of string, radius of bob, and length of hook
In a simple pendulum experiment, the length of the string, as measured by a metre scale, is 92.0 cm. The radius of the bob combined with the length of the hook, as measured by a vernier callipers, is 2.15 cm. The effective length of the pendulum is

•  94.1 cm
•  94.2 cm
•  94.15 cm
•  94 cm

Solution
(b)
( 92.0 + 2.15 ) cm = 94.15 cm. Rounding off to first decimal place, we get 94.2 cm

Q8. Given that Y=a sin⁡〖ωt + bt + ct² cos⁡ωt 〗. The unit of abc is same as that of

•  y
•  Ty / t
•  (y / t)²
•  (y / t)³

Solution

Q9. While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 2 % in the length of the pendulum and a negative error of 1 % in the value of time period. His actual percentage error in the measurement of the value of g will be

•  3 %
•  0 %
•  4 %
•  5 %

Solution

Q10. Dimensional formula of capacitance (or farad) is

•  M^-1 L^-2 T⁴ A²
•  M L² T⁴ A^-2
•  M L T^-4 A²
•  M^-1 L^-2 T^-4 A^-2

Solution