Home
Class 11
PHYSICS
Consider a home made vernier scale as sh...

Consider a home made vernier scale as shown in the figure. In this diagram, we are interested in measuring the length of the line PQ. If both the inclined are indentical and their angles are equal to `theta` then what is the least count of the instrument.

Text Solution

Verified by Experts

The correct Answer is:
`LC=l[(1-cos theta)/(cos theta)]`
Least count = 1 MSD - 1 VSD
`=(l)/(cos theta)-l`
`=((1-cos theta)/(cos theta))l`
Promotional Banner

Topper's Solved these Questions

  • ERROR AND MEASUREMENT

    ALLEN |Exercise Part-2(Exercise-2)(A)|16 Videos

  • ERROR AND MEASUREMENT

    ALLEN |Exercise Part-2(Exercise-2)(B)|22 Videos

  • ERROR AND MEASUREMENT

    ALLEN |Exercise Part-2(Exercise-2)(B)|22 Videos

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN |Exercise Exercise 5 B (Integer Type Questions)|3 Videos

  • KINEMATICS

    ALLEN |Exercise EXERCISE-2|89 Videos

Similar Questions

Explore conceptually related problems

Internal micrometer is a measuring intrument used to measure internal diameter (ID) of a large cylinder bore with high accuracy. Construction is shown in figure. There is one fixed rod B (to the right in figure) and one moved rod A (to the left in figure). It is based on the particle of advancement of a screw when it is rotated in a nut with internal threads. Main scale reading can be directly seen on the hub which is fixed with respect to rod B. When the cap is rotated rod A moves in or cut depending on direction of rotation. The circular scale reading is seen by checking which division of circular scale coincide with the references line This is to be multiplied by LC to get circular scale reading. Least count = value of 1 circular scale division = ("pitch")/("number of division on circular scale") Length of rod A is chosen to match the ID(PQ) to be measured. Zero error is checked by taking reading between standard blocks fixed at normal value of ID to be measured. Zero error is positive if cap end is one the right of the main scale and negative it is on the left side. In an internal micrometer, main scale division is of 0.5 mm and there are 50 divisions in circular scale. The least count of the instrument is-

In a specially designed vernier calipers, 10 divisions of the vernier scale are equal to 4 divisions of the main scale. In the following figure, the zero error and a measurement are shown. In the zero error, the 5^(th) and the 10^(th) divisions of the vernier coincides with 1 mm and 3 mm mark on the main scale respectively and in the measurement, the 2^(nd) and the 7^(th) divisions of the vernier scale coincide with the 23 mm and 25 mm mark on the main scale respectively as shown in the figure. Report the length measured with due regards to the error.

Internal micrometer is a measuring intrument used to measure internal diameter (ID) of a large cylinder bore with high accuracy. Construction is shown in figure. There is one fixed rod B (to the right in figure) and one moved rod A (to the left in figure). It is based on the particle of advancement of a screw when it is rotated in a nut with internal threads. Main scale reading can be directly seen on the hub which is fixed with respect to rod B. When the cap is rotated rod A moves in or cut depending on direction of rotation. The circular scale reading is seen by checking which division of circular scale coincide with the references line This is to be multiplied by LC to get circular scale reading. Least count = value of 1 circular scale division = ("pitch")/("number of division on circular scale") Length of rod A is chosen to match the ID(PQ) to be measured. Zero error is checked by taking reading between standard blocks fixed at normal value of ID to be measured. Zero error is positive if cap end is one the right of the main scale and negative it is on the left side. During zero setting of the above instrument, the end of the cap is on left side of the zero of main scale (i.e. zero of main scale is not visible) and 41^(th) division of circular scale coincides with the reference line, the zero error is -

Internal micrometer is a measuring intrument used to measure internal diameter (ID) of a large cylinder bore with high accuracy. Construction is shown in figure. There is one fixed rod B (to the right in figure) and one moved rod A (to the left in figure). It is based on the particle of advancement of a screw when it is rotated in a nut with internal threads. Main scale reading can be directly seen on the hub which is fixed with respect to rod B. When the cap is rotated rod A moves in or cut depending on direction of rotation. The circular scale reading is seen by checking which division of circular scale coincide with the references line This is to be multiplied by LC to get circular scale reading. Least count = value of 1 circular scale division = ("pitch")/("number of division on circular scale") Length of rod A is chosen to match the ID(PQ) to be measured. Zero error is checked by taking reading between standard blocks fixed at normal value of ID to be measured. Zero error is positive if cap end is one the right of the main scale and negative it is on the left side. In the above instrument, while measuring an internal diameter. ID is set of 321 mm with no zero error. It cap end is after n^(th) division adn 17^(th) division of main scale coincides with the reference line, the ID is -

Two identical balls A and B each of mass 0.1 kg are attached to two identical mass less is springs. The spring-mass system is constrained to move inside a right smooth pipe bent in the form of a circle as shown in figure . The pipe is fixed in a horizontal plane. The center of the balls can move in a circle of radius 0.06 m . Each spring has a natural length of 0.06 pi m and force constant 0.1 N//m . Initially, both the balls are displaced by an angle theta = pi//6 radians with respect to diameter PQ of the circle and released from rest. a. Calculate the frequency of oscillation of the ball B. b. What is the total energy of the system ? c. Find the speed of the ball A when A and B are at the two ends of the diameter PQ.

The bar shown in the figure is made of a single piece of material. It is fixed at one end and consists of two segments of equal length (L)/(2) but different cross-section area A and 2A. What is the change in length of the system under the action of an axial force F. [ consider the shape of joint to remain circular, Y is young's modulus] ltimg src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ALN_RACE_R64_E01_004_Q01.png" width="80%"gt

A physical quantity is a phyical property of a phenomenon , body, or substance , that can be quantified by measurement. The magnitude of the components of a vector are to be considered dimensionally distinct. For example , rather than an undifferentiated length unit L, we may represent length in the x direction as L_(x) , and so forth. This requirement status ultimately from the requirement that each component of a physically meaningful equation (scaler or vector) must be dimensionally consistent . As as example , suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity V_(x) and of widht D and he is swimming in direction perpendicular to the river flow with velocity V_(y) relation to river, assuming no use of directed lengths, the quantities of interest are then V_(x),V_(y) both dimensioned as (L)/(T) , S the drift and D width of river both having dimension L. with these four quantities, we may conclude tha the equation for the drift S may be written : S prop V_(x)^(a)V_(y)^(b)D^(c) Or dimensionally L=((L)/(T))^(a+b)xx(L)^(c) from which we may deduce that a+b+c=1 and a+b=0, which leaves one of these exponents undetermined. If, however, we use directed length dimensions, then V_(x) will be dimensioned as (L_(x))/(T), V_(y) as (L_(y))/(T), S as L_(x)" and " D as L_(y) . The dimensional equation becomes : L_(x)=((L_(x))/(T))^(a) ((L_(y))/(T))^(b)(L_(y))^(c) and we may solve completely as a=1,b=-1 and c=1. The increase in deductive power gained by the use of directed length dimensions is apparent. From the concept of directed dimension what is the formula for a range (R) of a cannon ball when it is fired with vertical velocity component V_(y) and a horizontal velocity component V_(x) , assuming it is fired on a flat surface. [Range also depends upon acceleration due to gravity , g and k is numerical constant]

ALLEN -ERROR AND MEASUREMENT-Part-2(Exercise-1)
  1. In a vernier calliper, N divisions of vernier scale coincide with (N-1...

    Text Solution

    |

  2. A vernier callipers having 1 main scale division = 0.1 cm to have a le...

    Text Solution

    |

  3. In a vernier callipers, N divisions of the main scale coincide with N ...

    Text Solution

    |

  4. In a vernier callipers the main scale and the vernier scale are made u...

    Text Solution

    |

  5. Consider the MB shown in the diagram, let the resistance X have temper...

    Text Solution

    |

  6. For a post office box, the graph of galvanometer deflection versus (R ...

    Text Solution

    |

  7. Identify which of the following diagrams represent the internal constr...

    Text Solution

    |

  8. In a meter bridge set up, which of the following should be the propert...

    Text Solution

    |

  9. The relative error in resistivity of a material where resistance = 1...

    Text Solution

    |

  10. In the searle's experiment, after every step of loading, why should we...

    Text Solution

    |

  11. Internal micrometer is a measuring intrument used to measure internal ...

    Text Solution

    |

  12. Internal micrometer is a measuring intrument used to measure internal ...

    Text Solution

    |

  13. Internal micrometer is a measuring intrument used to measure internal ...

    Text Solution

    |

  14. In a given slide callipers 10 division of its vernier coincides with i...

    Text Solution

    |

  15. Consider a home made vernier scale as shown in the figure. In this dia...

    Text Solution

    |

  16. The pitch of a screw gauge is 1 mm and there are 50 divisions on its c...

    Text Solution

    |

  17. A short circuit occurs in a telephone cable having a resistance of 0.4...

    Text Solution

    |

  18. A glass prism of angle A = 60^(@) gives minimum angle of deviation the...

    Text Solution

    |

  19. In a given optical bench, a needle of length 10 cm is used to estimate...

    Text Solution

    |

  20. Consider S = X cos (theta) for X = (2.0 pm 0.2) cm, theta = 53 pm 2^(@...

    Text Solution

    |