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If \( 50 \) Vernier divisions are equal to \( 49 \) main scale division of a traveling microscope and one smallest reading of main scale is \( 0.5 \, \text{mm} \), the Vernier constant of traveling microscope is:

If the percentage errors in measuring the length and the diameter of a wire are \( 0.1\% \) each. The percentage error in measuring its resistance will be:

The resistance \( R = \frac{V}{I} \) where \( V = (200 \pm 5) \, \text{V} \) and \( I = (20 \pm 0.2) \, \text{A} \), the percentage error in the measurement of \( R \) is:

Young's modulus is determined by the equation given by \( Y = 49000 \, \frac{m}{l} \, \text{dyne} / \text{cm}^2 \) where \( M \) is the mass and \( l \) is the extension of wire used in the experiment. Now error in young modules (\( Y \)) is estimated by taking data from \( M\text{–}l \) plot in graph paper. The smallest scale divisions are \( 5 \, \text{g} \) and \( 0.02 \, \text{cm} \) along load axis and extension axis respectively. If the value of \( M \) and \( l \) are \( 500 \, \text{g} \) and \( 2 \, \text{cm} \) respectively then percentage error of \( Y \) is:

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its \( 4^{\text{th}} \) division coincides exactly with a certain division on main scale. If \( 50 \) vernier scale divisions equal to \( 49 \) main scale divisions and zero error in the instrument is \( 0.04 \, \text{mm} \) then how many main scale divisions are there in \( 1 \, \text{cm} \)?

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as \( 4.62 \, \text{s} \), \( 4.632 \, \text{s} \), \( 4.6 \, \text{s} \) and \( 4.64 \, \text{s} \). The arithmetic mean of these readings in correct significant figure is:

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

A physical quantity \( Q \) is found to depend on quantities \( a, b, c \) by the relation \( Q = \dfrac{a^{4} b^{3}}{c^{2}} \). The percentage error in \( a, b \) and \( c \) are \( 3\% \), \( 4\% \) and \( 5\% \) respectively, Then, the percentage error in \( Q \) is:

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 \( 1 \, \text{mm} \). The main scale reading is \( 2 \, \text{cm} \) and second division of vernier scale coincides with a division on main scale. If mass of the sphere is \( 8.635 \, \text{g} \), the density of the sphere is:

In an experiment to measure focal length \( (f) \) of convex lens, the least counts of the measuring scales for the position of object \( (u) \) and for the position of image \( (v) \) are \( \Delta u \) and \( \Delta v \), respectively. The error in the measurement of the focal length of the convex lens will be:

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \( 1 \, \text{mm} \) and circular scale reading is equal to \( 42 \) divisions. Pitch of screw gauge is \( 1 \, \text{mm} \) and it has \( 100 \) divisions on circular scale. The diameter of the wire is \( \dfrac{x}{50} \, \text{mm} \). The value of \( x \) is:

A vernier callipers has \( 20 \) divisions on the vernier scale, which coincides with \( 19^{\text{th}} \) division on the main scale. The least count of the instrument is \( 0.1\,\text{mm} \). One main scale division is equal to _____ \( \text{mm} \).

Identify the physical quantity that cannot be measured using spherometer:

The radius \( (r) \), length \( (l) \) and resistance \( (R) \) of a metal wire was measured in the laboratory as
\( r = (0.35 \pm 0.05) \, \text{cm} \)
\( R = (100 \pm 10) \, \text{ohm} \)
\( l = (15 \pm 0.2) \, \text{cm} \)
The percentage error in resistivity of the material of the wire is:

To find the spring constant \((k) \) of a spring experimentally, a student commits \( 2\% \) positive error in the measurement of time and \( 1\% \) negative error in measurement of mass. The percentage error in determining value of \( k \) is:

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 give below:

In finding out refractive index of glass slab the following observations were made through travelling microscope \( 50 \) vernier scale division \( = 49 \) MSD; \( 20 \) divisions on main scale in each \( \text{cm} \)
For mark on paper
MSR \( = 8.45 \, \text{cm} \), VC \( = 26 \)
For mark on paper seen through slab
MSR \( = 7.12 \, \text{cm} \), VC \( = 41 \)
For powder particle on the top surface of the glass slab
MSR \( = 4.05 \, \text{cm} \), VC \( = 1 \)
(MSR \( = \) Main Scale Reading, VC \( = \) Vernier Coincidence)
Refractive index of the glass slab is:

\( 10 \) divisions on the main scale of a vernier calliper coincide with \( 11 \) divisions on the Vernier scale. If each division on the main scale is of \( 5 \) units, the least count of the instrument is:

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JEE Main 2024 29th Jan Morning Shift

The resistance \( R = \frac{V}{I} \) where \( V = (200 \pm 5) \, \text{V} \) and \( I = (20 \pm 0.2) \, \text{A} \), the percentage error in the measurement of \( R \) is: