Q. No.In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \(100\) divisions in circular scale and pitch of screw gauge is \(0.1~\text{mm}.\) When diameter of a sphere is measured, the reading of main scale is \(5~\text{mm}\) and \(50^\text{th}\) division of circular scale coincides with the reference line of main scale. The diameter of sphere is: (in mm)
1. \(5.045\)
2. \(5.055\)
3. \(5.450\)
4. \(5.550\)
1. \(5.045\)
2. \(5.055\)
3. \(5.450\)
4. \(5.550\)
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In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \(7^{\text{th}}\) Vernier division coincides with a main scale reading. If the value of \(1\) main scale division is \(1\) mm and there are \(10\) Vernier scale divisions, then the Vernier caliper has:
1. \(0.07\) cm negative zero error
2. \(0.7\) cm negative zero error
3. \(0.07\) cm positive zero error
4. \(0.7\) cm positive zero error
1. \(0.07\) cm negative zero error
2. \(0.7\) cm negative zero error
3. \(0.07\) cm positive zero error
4. \(0.7\) cm positive zero error
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In a screw gauge when the circular scale is given five complete rotations, it moves linearly by \(2.5~\text{mm}\). If the circular scale has \(100\) divisions, the least count of screw gauge is (in mm):
1. \(1\times10^{-2}\)
2. \(1\times 10^{-3}\)
3. \(5\times 10^{-2}\)
4. \(5\times 10^{-3}\)
1. \(1\times10^{-2}\)
2. \(1\times 10^{-3}\)
3. \(5\times 10^{-2}\)
4. \(5\times 10^{-3}\)
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In a screw gauge, the zero of the circular scale lies \(3\) divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is \(1\) mm and the circular scale reading is \(51\) then the correct thickness of the sheet is: (in mm)
[Assume least count is \(0.01\) mm]
1. \(1.50\)
2. \(1.48\)
3. \(1.54\)
4. \(1.51\)
[Assume least count is \(0.01\) mm]
1. \(1.50\)
2. \(1.48\)
3. \(1.54\)
4. \(1.51\)
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In a vernier callipers, \(50\) vernier scale division are equal to \(48\) main scale division. If one main scale division \(=0.05 ~\text{mm},\) mm, then the last count of the vernier callipers is: (in mm)
1. \(0.002\)
2. \(0.05\)
3. \(0.02\)
4. \(0.005\)
1. \(0.002\)
2. \(0.05\)
3. \(0.02\)
4. \(0.005\)
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When both jaws of vernier callipers touch each other, mark of the vernier scale is right to zero mark of main scale, \(4^\text {th}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes \(15\) divisions on main scale and \(5^\text {th}\) division of vernier scale coincides with a min scale division. Measured length of cylinder is: (in mm). (Least count of Vernier calliper = \(0.1~\text{mm}\))
1. \(15.4\)
2. \(15.1\)
3. \(15.5\)
4. \(15.9\)
1. \(15.4\)
2. \(15.1\)
3. \(15.5\)
4. \(15.9\)
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In an experiment, a set of readings are obtained; \(1.24~\text{mm}, 1.25~\text{mm}, 1.23~\text{mm}, 1.21~\text{mm}\). The expected least count of the instrument used in recording these readings is: (in mm)
1. \(0.01\)
2. \(0.001\)
3. \(0.1\)
4. \(0.05\)
1. \(0.01\)
2. \(0.001\)
3. \(0.1\)
4. \(0.05\)
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For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains \(300\) equal divisions equals to \(15 ~\text{cm.}\) The Vernier scale attached to the microscope has \(25\) divisions equals to \(24\) divisions of main scale. The least count \((LC) \) of the travelling microscope is (in cm):
1. \(0.0005\)
2. \(0.0025\)
3. \(0.002\)
4. \(0.001\)
1. \(0.0005\)
2. \(0.0025\)
3. \(0.002\)
4. \(0.001\)
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The least count of a screw gauge is \(0.01~\text{mm}.\) If the pitch is increased by \(75\%\) and number of divisions on the circular scale is reduced by \(50\%,\) the new least count will be:
1. \(64 \times 10^{-3} ~\text{mm}\)
2. \(35 \times 10^{-3} ~\text{mm}\)
3. \(77 \times 10^{-3} ~\text{mm}\)
4. \(15 \times 10^{-3} ~\text{mm}\)
1. \(64 \times 10^{-3} ~\text{mm}\)
2. \(35 \times 10^{-3} ~\text{mm}\)
3. \(77 \times 10^{-3} ~\text{mm}\)
4. \(15 \times 10^{-3} ~\text{mm}\)
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Given below are two statements:
In the light of the above statements, choose the correct answer from the option given below
| Statement-I: | In a Vernier calipers, one Vernier scale division is always smaller than one main scale division. |
| Statement-II: | The Vernier constant is given by one main scale division multiplied by the number of Vernier scale divisions |
| 1. | Statement-I is true but statement-II is false |
| 2. | Both Statement-I and Statement-II are true |
| 3. | Statement-I is false but statement-II is true |
| 4. | Both Statement-I and Statement-II are false |
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