Question

A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of $0.5\mathrm{mm}$ is noticed on the pitch scale. The nature of zero error involved and the lest count of the screw gauge, are respectively:

JEE Main 2020 (06 Sep Shift 1)

Options

• A: Negative, $2\mu \mathrm{m}$
• B: Positive $10\mu \mathrm{m}$
• C: Positive $0.1m\mathrm{m}$
• D: Positive, $0.1\mu m$

Question

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings $5.50 \mathrm{mm}$, $5.55 \mathrm{mm}$, $5.34 \mathrm{mm}$, $5.65 \mathrm{mm}$. The average of these four reading is $5.5375 \mathrm{mm}$ and the standard deviation of the data is $0.07395 \mathrm{mm}$. The average diameter of the pencil should therefore be recorded as :

JEE Main 2020 (06 Sep Shift 2)

Options

• A: $\left(5.5375\pm 0.0739\right)\mathrm{mm}$
• B: $\left(5.5375\pm 0.0740\right)\mathrm{mm}$
• C: $\left(5.538\pm 0.074\right)\mathrm{mm}$
• D: $\left(5.54\pm 0.07\right)\mathrm{mm}$

Question

Student $A$ and student $B$ used two screw gauges of equal pitch and $100$ equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is $0.322 \mathrm{cm}$. The absolute value of the difference between the final circular scale readings observed by the students $A$ and $B$ is _______.

[Figure shows position of reference $O$ when jaws of screw gauge are closed]

Given pitch $=0.1 \mathrm{cm}$.

JEE Main 2021 (25 Jul Shift 1)

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Question

A screw gauge of pitch $0.5 \mathrm{mm}$ is used to measure the diameter of uniform wire of length $6.8 \mathrm{cm}$, the main scale reading is $1.5 \mathrm{mm}$ and circular scale reading is $7$. The calculated curved surface area of wire to appropriate significant figures is
[Screw gauge has $50$ divisions on the circular scale]

JEE Main 2022 (26 Jul Shift 1)

Options

• A: $6.8{ \mathrm{cm}}^2$
• B: $3.4{ \mathrm{cm}}^2$
• C: $3.9{ \mathrm{cm}}^2$
• D: $2.4{ \mathrm{cm}}^2$

Question

In a Vernier Caliper $10$ divisions of Vernier scale is equal to the $9$ divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and $4^{\mathrm{th}}$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $1 \mathrm{mm}$. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between $30$ and $31$ divisions of main scale reading and $6^{\mathrm{th} }$ Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be:

JEE Main 2022 (26 Jul Shift 2)

Options

• A: $3.02 \mathrm{cm}$
• B: $3.06 \mathrm{cm}$
• C: $3.10 \mathrm{cm}$
• D: $3.20 \mathrm{cm}$

Question

In an experiment to find out the diameter of wire using screw gauge, the following observation were noted:

(a) Screw moves $0.5 \mathrm{mm}$ on main scale in one complete rotation
(b) Total divisions on circular scale $=50$
(c) Main scale reading is $2.5 \mathrm{mm}$
(d) ${45}^{\mathrm{th}}$${ }^{}$ division of circular scale is in the pitch line
(e) Instrument has $0.03 \mathrm{mm}$ negative error Then the diameter of wire is :

JEE Main 2022 (29 Jul Shift 1)

Options

• A: $2.92 \mathrm{mm}$
• B: $2.54 \mathrm{mm}$
• C: $2.98 \mathrm{mm}$
• D: $3.45 \mathrm{mm}$

Question

In an experiment with vernier callipers of least count $0.1 \mathrm{mm}$, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and $6^{\mathrm{th}}$ division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between $3.2 \mathrm{cm}$ and $3.3 \mathrm{cm}$ marks and $4^{\mathrm{th}}$ division of vernier scale coincides with the main scale division. The diameter of bob is measured as

JEE Main 2023 (10 Apr Shift 2)

Options

• A: $3.22 \mathrm{cm}$
• B: $3.18 \mathrm{cm}$
• C: $3.26 \mathrm{cm}$
• D: $3.25 \mathrm{cm}$

Question

In a metre bridge experiment the balance point is obtained if the gaps are closed by $2 \mathrm{\Omega }$ and $3 \mathrm{\Omega }$. A shunt of $X \mathrm{\Omega }$ is added to $3 \mathrm{\Omega }$ resistor to shift the balancing point by $22.5 \mathrm{cm}$. The value of $X$ is ______.

JEE Main 2023 (29 Jan Shift 1)

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Question

In a screw gauge, there are $100$ divisions on the circular scale and the main scale moves by $0.5 \mathrm{mm}$ on a complete rotation of the circular scale. The zero of circular scale lies $6$ divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, $4$ linear scale divisions are clearly visible while 46^th division the circular scale coincide with the reference line. The diameter of the wire is ______ $\times {10}^{-2} \mathrm{mm}.$

JEE Main 2023 (30 Jan Shift 1)

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Question

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1 \mathrm{~mm}$. The main scale reading is $2 \mathrm{~cm}$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:

JEE Main 2024 (08 Apr Shift 1)

Options

• A: $2.0 \mathrm{~g} / \mathrm{cm}^3$
• B: $1.7 \mathrm{~g} / \mathrm{cm}^3$
• C: $2.2 \mathrm{~g} / \mathrm{cm}^3$
• D: $2.5 \mathrm{~g} / \mathrm{cm}^3$

Question

There are 100 divisions on the circular scale of a screw gauge of pitch $1 \mathrm{~mm}$. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :

JEE Main 2024 (08 Apr Shift 2)

Options

• A: $3.35 \mathrm{~mm}$
• B: $4.65 \mathrm{~mm}$
• C: $4.55 \mathrm{~mm}$
• D: $4.60 \mathrm{~mm}$

Question

Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R).
Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.
In the light of the above statements, choose the correct answer from the options given below :

JEE Main 2024 (27 Jan Shift 2)

Options

• A: Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B: Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C: (A) is true but (R) is false
• D: (A) is false but (R) is true

Question

The measured value of the length of a simple pendulum is $20 \mathrm{cm}$ with $2 \mathrm{mm}$ accuracy. The time for $50$ oscillations was measured to be $40$ seconds with $1$ second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $N\%$. The value of $N$ is:

JEE Main 2024 (31 Jan Shift 2)

Options

• A: $4$
• B: $8$
• C: $6$
• D: $5$