Screw Gauge

Q. The least count of the main scale of a vernier callipers is $1\text{mm}$. Its vernier scale is divided into $10$ divisions and coincide with $9$ divisions of the main scale. When jaws are touching each other, the $7^{\text{th}}$ division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between $3.1\text{cm}$ and $3.2\text{cm}$ and $4^{\text{th}}\text{VSD}$ coincides with a main scale division. The length of the cylinder is $(\text{VSD}$ is vernier scale division$)$

1. $3.21\text{cm}$
2. $3.07\text{cm}$
3. $3.21\text{cm}$
4. $2.99\text{cm}$

Q. The least count of the main scale of a screw gauge is $1\text{mm}$. The minimum number of divisions on its circular scale required to measure $5\mu \text{m}$ diameter of a wire is:

1. $100$
2. $50$
3. $500$
4. $200$

Q. In a screw gauge, the fifth division of the circular scale coincides with the reference line, when the ratchet is closed. There are $50$ divisions on the circular scale, and the main scale moves by $0.5\text{mm}$ on a complete rotation. For a particular observation, the reading on the main scale is $5\text{mm}$ and the ${20}^{\text{th}}$ division of the circular scale coincides with the reference line. Calculate the true reading.

1. $5.20\text{mm}$
2. $5.25\text{mm}$
3. $5.15\text{mm}$
4. $5.00\text{mm}$

Q. The diameter of the spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of the vernier scale. One main scale division is $1\text{mm}$. The main scale reading is $10\text{mm}$ and $8^{th}$ 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 $0.04\text{cm}$, then the radius of the bob is ____
$\times {10}^{-2}\text{cm}$.

Q. A screw gauge gives the following reading for measuring the diameter of a wire.
Main scale reading : $0\text{mm}$
Circular scale reading : $60$ divisions
Given, that $1\text{mm}$ on main scale corresponds to $100$ divisions on circular scale. The diameter of wire is,

1. $0.050\text{cm}$
2. $0.054\text{cm}$
3. $0.062\text{cm}$
4. $0.060\text{cm}$

Q. When the gap is closed without placing any object in the screw gauge whose least count is $0.005\text{mm}$, the $5^{th}$ division on its circular scale coincides with the reference line on main scale. When a small sphere is placed, the reading on the main scale advances by 4 divisions, whereas the ${25}^{th}$ division on its circular scale coincides with the reference line on the main scale. There are 200 divisions on the circular scale. The radius of the sphere measured is

1. $4.10\text{mm}$
2. $4.05\text{mm}$
3. $2.10\text{mm}$
4. $2.05\text{mm}$

Q. $\text{Assertion A}$ : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is $5\text{mm}$ and there are $50$ total divisions on circular scale, then least count is $0.001\text{cm}$.

$\text{Reason R}$ :
$\text{Least Count}=\frac{\text{Pitch}}{\text{Total divisions on circular scale}}$

In the light of the above statements, choose the most appropriate answer from the options given below :

1. $\text{A}$ is not correct but $\text{R}$ is correct.
2. Both $\text{A}$ and $\text{R}$ are correct and $\text{R}$ is the correct explanation of $\text{A}$.
3. $\text{A}$ is correct but $\text{R}$ is not correct.
4. Both $\text{A}$ and $\text{R}$ are correct and $\text{R}$ is NOT the correct explanation of $\text{A}$.

Q. The pitch of a screw gauge is $2\text{mm}$ and there are $100$ divisions on the circular scale. In measuring the diameter of a sphere, there are $6$ divisions on the linear scale and $40$ divisions on circular scale coinciding with the reference line. The diameter of the sphere is:

1. $6.4\text{mm}$
2. $12.8\text{mm}$
3. $3.2\text{mm}$
4. $20\text{mm}$

Q. In a screw gauge, $5$ complete rotations of circular scale give \$1.5mm$ reading on linear scale. Circular scale has $50$ divisions. The least count of the screw gauge is $x\times {10}^y$$\left(mm\right)$. Find $(x+y)$.

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


(A) Screw moves $0.5\text{mm}$ on main scale in one complete rotation
(B) Total divisions on circular scale $=50$
(C) Main scale reading is $2.5\text{mm}$
(D) ${45}^{\text{th}}$ division of circular scale is in the pitch line
(E) Instrument has $0.03\text{mm}$ negative error

Then the diameter of wire is:

Q. The pitch of a screw gauge is $1\text{mm}$ and there are $100$ divisions on circular scale. When the faces $A$ and $B$ are just touching each without putting anything between the studs, the ${32}^{\text{nd}}$ division of the circular scale coincides with the reference line. The error in measurement due to screw gauge will be (zero of linear scale is not hidden from circular scale when $A$ and $B$ touches)

1. $-0.04\text{mm}$
2. $+0.32\text{mm}$
3. $+0.16\text{mm}$
4. $+0.04\text{mm}$

Q. The least counts of a vernier calipers and a screw gauge are in the ratio of 5 : 1. The main scales ofboth the instruments are marked in mm. The zero error on the vernier calipers is +0.15 mm where as that on screw gauge is –0.06 mm. If the diameter of a rod lies between 0.9 cm and 1.0 cm, and x and y are the VCD and CSR on the two instruments, relation between x and y given that the number of C.S.D. = 100, is

Q. The diameter of a wire is measured with a screw gauge having $50$ divisions on circular scale and by one complete rotation of circular scale, main scale moves $0.5\text{mm}$. If reading of screw gauge is $0.250\text{cm}$. The minimum percentage error in the reading will be

1. $0.4$
2. $0.8$
3. $4$
4. $5$

Q. The orbital electron of the hydrogen atom jumps from the ground state to a higher energy state and its orbital velocity is reduced to one third of its initial value. If the radius of the orbit in ground state is $r$, what is the radius of new orbit?

1. $2r$
2. $3r$
3. $4r$
4. $9r$

Q. The pitch of a screw gauge is $1mm$ and there are $100$ divisions on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies $6$ divisions below the reference line. When a wire is placed between the jaws, $2$ linear scale divisions are clearly visible while $62$ divisions on circular scale coincide with the reference line. Determine the diameter of the wire.

1. Measured reading is 2.56 mm.
2. Measured reading is 2.62 mm.
3. True reading is 2.62 mm.
4. True reading is 2.56 mm.

Q.

What is the least count of screw gauge?

1. $0$

2. $0.1mm$

3. $0.01mm$

4. $0.001mm$

Q. If the radius of the first orbit of the hydrogen atom is $5.29\times {10}^{-11}\text{m},$ the radius of the second orbit will be

1. $21.16\times {10}^{-11}\text{m}$
2. $10.58\times {10}^{-11}\text{m}$
3. $15.87\times {10}^{-11}\text{m}$
4. $2.64\times {10}^{-11}\text{m}$

Q. A magnet performs 10 oscillations per minute in a horizontal plane at a place where the angle of dip is 45^0 and the total intensity is 0.707 CGS units.The number of oscillations per minute at a place where dip angle is 60^° and total intensity is 05 CGS units will be(a) 5(c) 9(b) 7(d) 11

Q. The diameter of the spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of the vernier scale. One main scale division is $1\text{mm}$. The main scale reading is $10\text{mm}$ and $8^{th}$ 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 $0.04\text{cm}$, then the radius of the bob is

1. $36\times {10}^{-2}\text{cm}$
2. $52\times {10}^{-2}\text{cm}$
3. $48\times {10}^{-2}\text{cm}$
4. $55.6\times {10}^{-2}\text{cm}$

Q. Find the least count of a screw gauge whose least count of linear scale is 1mm and the circular scale is divided in 50 divisions and 2 entire rotations makes to 1 division on linear scale.

Q.

In a Searle's experiment, the diameter of the wire as measured by a screw gauge with least count 0.001 cm is 0.050 cm. The length, measured by a scale of least count 0.1 cm, is 110.0 cm. When a weight of 50 N is suspended from the wire, the extension is measured to be 0.125 cm by a micrometer of least count 0.001 cm. Find the maximum error in the measurement of Young's modulus of the material of the wire from these data.

$y=\frac{W}{A}\times \frac{L}{X}$
Where W is the weight suspended from the wire, A is the cross section area, L is the length and X is the extension in the wire.

[IIT JEE 2004]

1. 15.56 %

2. 4.89 %

3. 1.26 %

4. 9.67 %

Q. What is negative zero error of screw gauge?

Q. The pitch of a screw gauge is $1\text{mm}$ and there are $100$ divisions on circular scale. When the faces $A$ and $B$ are just touching each without putting anything between the studs, the ${32}^{\text{nd}}$ division of the circular scale coincides with the reference line. The error in measurement due to screw gauge will be (zero of linear scale is not hidden from circular scale when $A$ and $B$ touches)

1. $+0.32\text{mm}$
2. $-0.04\text{mm}$
3. $+0.16\text{mm}$
4. $+0.04\text{mm}$

Q. Screw gauge of pitch $0.1\text{cm}$ and $50$ divisions on circular scale measures thickness of an object. Which of the following measurement is possible for thickness?

1. $2.123\text{cm}$
2. $2.124\text{cm}$
3. $2.125\text{cm}$
4. $2.127\text{cm}$

Q.

Find the least count of a screw gauge whose least count of linear scale is 1 mm and the circular scale is divided in 50 divisions and 2 entire rotations makes to 1 division on linear scale.

1. 0.1mm

2. 0.01 mm

3. 0.02 mm

4. 0.2 mm

Q. Diameter of a wire measured by a screw guage in four different readings is found to be 2.20 mm, 2.10 mm, 2.40 mm and 1.90 mm.

1. Number of significant figures in all readings is two.

2. Error in $1^{st}$ reading is negative.
3. Mean error of readings is zero.
4. Error in $4^{th}$ reading is 0.25 mm.

Q. A screw gauge having $100$ equal divisions and a pitch length of $1\text{mm}$ is used to measure the diameter of a wire of length $5.6\text{cm}$. The main scale reading is $1\text{mm}$ and ${47}^{\text{th}}$ circular division coincides with the main scale. The curved surface area of wire (in ${\text{cm}}^2$) to appropriate significant figures is

1. $1.60$
2. $3.20$
3. $1.25$
4. $2.6$

Q. 26.two small dipole are placed in space as shown dipole p1 is fixed and p2 is allowed to rotate about its hinged centre find the direction of rotation of p2 in the following cases

Q. What is the meaning of zero of circular scale division coincides with 25 divisions above reference level in screw gauge ?what is difference if it was written below in place of above?

Q. A screw gauge has some zero error. Least count of this gauge is 0.01mm. 95th division of cap scale coincides with reference line when the gap is closed. What is the zero correction for this instrument ?