Answer following : (a) You are given a thread and a metre scale. How will you estimate diameter of t

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1.Units, Dimensions and Measurement

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Answer the following :

$(a)$ You are given a thread and a metre scale. How will you estimate the diameter of the thread ?

$(b)$ A screw gauge has a pitch of $1.0\; mm$ and $200$ divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale ?

$(c)$ The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of $100$ measurements of the diameter expected to yield a more reliable estimate than a set of $5$ measurements only ?

Option A

Option B

Option C

Option D

Solution

Wrap the thread on a uniform smooth rod in such a way that the coils thus formed are very close to each other. Measure the length of the thread using a metre scale. The diameter of the thread is given by the relation,

Diameter $=\frac{\text { Length of thread }}{\text { Number of turns }}$

It is not possible to increase the accuracy of a screw gauge by increasing the number of divisions of the circular scale. Increasing the number divisions of the circular scale will increase its accuracy to a certain extent only.

A set of $100$ measurements is more reliable than a set of $5$ measurements because random errors involved in the former are very less as compared to the latter.

Standard 11

Physics

A screw gauge gives the following reading when used to measure the diameter of a wire.

Main scale reading : $0\ mm$

Circular scale reading : $52\ divisions$

Given that $1\ mm$ on main scale corresponds to $100$ divisions of the circular scale. The diameter of wire from the above data is:

medium

(AIEEE-2011)

A student measured the length of a rod and wrote it as $3.50\;cm$. Which instrument did he use to measure it?

medium

(JEE MAIN-2014)

One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text {th }}$ division of main scale coincides with $(n+1)^{\mathrm{th}}$ division of vernier scale, the least count of the vernier caliper is:

hard

(JEE MAIN-2024)

The diameter of a spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of vernier scale. One main scale division is $1\, {mm}$. The main scale reading is $10\, {mm}$ and $8^{\text {th }}$ division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of $0.04\, {cm}$, then the radius of the bob is $…… \,\times 10^{-2} \,{cm}$

hard

(JEE MAIN-2021)

The vernier scale used for measurement has a positive zero error of $0.2\, mm$. If while taking a measurement it was noted that $'0'$ on the vernier scale lies between $8.5\, cm$ and $8.6\, cm$ vernier coincidence is $6,$ then the correct value of measurement is …………. $cm$. (least count $=0.01\, cm )$

medium

(JEE MAIN-2021)

Solution

Similar Questions

A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : $0\ mm$ Circular scale reading : $52\ divisions$ Given that $1\ mm$ on main scale corresponds to $100$ divisions of the circular scale. The diameter of wire from the above data is:

A student measured the length of a rod and wrote it as $3.50\;cm$. Which instrument did he use to measure it?

One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text {th }}$ division of main scale coincides with $(n+1)^{\mathrm{th}}$ division of vernier scale, the least count of the vernier caliper is:

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A screw gauge gives the following reading when used to measure the diameter of a wire.

Main scale reading : $0\ mm$

Circular scale reading : $52\ divisions$

Given that $1\ mm$ on main scale corresponds to $100$ divisions of the circular scale. The diameter of wire from the above data is: