Error and Uncertainty

Q.

In the determination of Young’s modulus $(Y=\frac{4MLg}{\pi l{d}^2})$ by using Searle’s method, a wire of length L=2m and diameter d=0.5mm is used. For a load M=2.5kg, an extension l=0.25mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement is:

1. Due to the errors in the measurement of d and l are the same

2. Due to the error in the measurement of d is twice that due to the error in the measurement of l

3. Due to the error in the measurement of l is twice that due to the error in the measurement of d

4. Due to the error in the measurement of d is four times that due to the error in the measurement of l

Q.

Two full turns of the circular scale of a screw gauge cover a distance of $1mm$ on its main scale. The total number of divisions of $1mm$on its main scale. The total number of divisions on the circular scale is $50$. Further, it is found that the screw guage has a zero error of $-0.03mm$. While measuring the diameter of a thin wire, a student notes the main scale reading of $3mm$and the number of circular scale divisions in line with the main scale as $35$. The diameter of the wire is

1. $3.32mm$

2. $3.73mm$

3. $3.67mm$

4. $3.88mm$

Q. Two blocks of mass m, 2m connected with spring are placed on smooth horizontal surface. A uniform horizontal force F starts acting on block of mass 2m as shown. Elongation in spring when acceleration of each block is same, is

स्प्रिंग द्वारा संयोजित m व 2m द्रव्यमान के दो गुटकों को एक चिकने क्षैतिज पृष्ठ पर रखा जाता है। 2m द्रव्यमान के गुटके पर एकसमान क्षैतिज बल F दर्शाए अनुसार कार्य करना प्रारम्भ करता है। जब प्रत्येक गुटके का त्वरण समान है, तब स्प्रिंग में प्रसार है

1. $\frac{F}{3k}$
   
2. $\frac{2F}{3k}$
   
3. $\frac{F}{4k}$
   
4. $\frac{F}{2k}$
   

Q.

The main scale reading is 8 cm and vernier coincidence is 4 and negative zero error is 0.02 cm. Then calculate the correct reading:
[2marks]

Q. The least count of a screw gauge can be practically decreased by _________________.

1. increasing the total number of divisions on the main scale

2. decreasing the total number of divisions on the circular scale

3. increasing the total number of divisions on the circular scale

4. constructing the gauge with an alloy of iron, tin, and lead

Q. The screw of a screw gauge moves $4.5mm$ linearly for every $3$ complete rotations of the ratchet. If the circular scale of the gauge has $95$ divisions, the least count of the screw gauge is:

1. $0.0158cm$
2. $0.00158cm$
3. $1.58\mu m$
4. $15.8\mu m$

Q. Zero error of an instrument introduces:

1. Both
2. Systematic errors
3. Random errors
4. None

Q. The accuracy of measurement also lies in the way the result is expressed. The number of digits to which a value is to be expressed is one digit more than number of sure numbers. Rules do exist to deal with number of digits after an operation is carried out on the given values. The error can be minimised by many trials and using the correct methods and instruments.
The number of significant figures can reduces in

1. Multiplication
2. Addition
3. Subtraction
4. Division

Q. The smallest division on the main scale of a vernier callipers is $1\text{mm}$ and $10$ vernier divisions coincide with $9$ main scale divisions. While measuring the length of a line, the zero mark of the vernier scale lies between $10.2\text{cm}$ and $10.3\text{cm}$ and the third division of the vernier scale coincides with a main scale division.
(a) Determine the least count of the callipers.
(b) Find the length of the line.

Q. A screw gauge with a pitch of $0.5\text{mm}$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the ${45}^{\text{th}}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5\text{mm}$ and the ${25}^{\text{th}}$ division coincides with the main scale line?

Q. If the length of a simple pendulum at a given place is increased by 6 times, the ratio of the final to the initial time periods of the pendulum is .

1. $36:1$
2. $1:\sqrt{6}$
3. $\sqrt{6}:1$
4. $1:36$