Experimental Skills — JEE Main PYQs

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 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and $50^{\text{th}}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is ________ mm.

In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If the circular scale has 100 divisions, the least count of screw gauge is _________ mm.

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

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as $10 \text{ V}$ and $5 \text{ A}$, respectively. The least counts of voltmeter and ammeter are $500 \text{ mV}$ and $200 \text{ mA}$, respectively. The estimated error in the resistance measurement is __________ $\Omega$

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to $15 \mathrm{~cm}$. 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) :

Given below are two statements :

Statement I : In a vernier callipers, 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.

In the light of the above statements, choose the correct answer from the options given below.

In the experiment for measurement of viscosity '$\eta$' of given liquid with a ball having radius R, consider following statements.

A. Graph between terminal velocity V and R will be a parabola.

B. The terminal velocities of different diameter balls are constant for a given liquid.

C. Measurement of terminal velocity is dependent on the temperature.

D. This experiment can be utilized to assess the density of a given liquid.

E. If balls are dropped with some initial speed, the value of $\eta$ will change.

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where $x$ 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 :

To measure the internal resistance of a battery, potentiometer is used. For R = 10 Ω, the balance point is observed at $l = 500$ cm and for R = 1 Ω the balance point is observed at $l = 400$ cm. The internal resistance of the battery is approximately :

Which of the diode circuit shows correct biasing used for the measurement of dynamic resistance of p-n junction diode :

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $\frac{1}{\theta}$ vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is ________ $\times 10^{-1}$ A/division. [The source has emf 2V]

[Figure: straight-line graph of $\frac{1}{\theta}\ (\mathrm{div}^{-1})$ on the y-axis (markings at ½, 1, 1½, 2) versus $R\ (\Omega)$ on the x-axis (markings at 2, 4, 6); dashed lines indicate points near (2, 1), (4, 1½) and (6, 2)]

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 mm. One main scale division is equal to ________ mm.

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is $\frac{x}{50}\ mm$. The value of $x$ 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 mm then how many main scale divisions are there in 1 cm ?

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 cm

For mark on paper

$\mathrm{MSR} = 8.45\ \mathrm{cm},\ \mathrm{VC} = 26$

For mark on paper seen through slab

$\mathrm{MSR} = 7.12\ \mathrm{cm},\ \mathrm{VC} = 41$

For powder particle on the top surface of the glass slab

$\mathrm{MSR} = 4.05\ \mathrm{cm},\ \mathrm{VC} = 1$

(MSR = Main Scale Reading, VC = Vernier Coincidence)

Refractive index of the glass slab is :

Young's modulus is determined by the equation given by $Y = 49000\,\frac{m}{l}\ \frac{\text{dyne}}{\text{cm}^2}$ 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 $M$-$l$ plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of $M$ and $l$ are 500 g and 2 cm respectively then percentage error of $Y$ 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 mm. The main scale reading is 2 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:

There are 100 divisions on the circular scale of a screw gauge of pitch 1 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 :

Least count of a vernier caliper is $\frac{1}{20\mathrm{N}}$ cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale 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 :

To determine the resistance ($R$) of a wire, a circuit is designed below. The $V$-$I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is __________ $\Omega$.

[Figure: circuit — a voltmeter V of internal resistance 10 kΩ connected in parallel with resistance R, in series with a milliammeter (mA) and a variable source E; below it a graph of $I$(mA) versus $V$(volt) showing a straight line through the origin passing through points (4, 2), (6, 3) and (8, 4)]

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 :

In a metre-bridge when a resistance in the left gap is 2 $\Omega$ and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with 2 $\Omega$, the balance length changes by :

Identify the physical quantity that cannot be measured using spherometer :

A wire of length 10 cm and radius $\sqrt{7} \times 10^{-4}$ m is connected across the right gap of a meter bridge. When a resistance of $4.5\ \Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is $\mathrm{R} \times 10^{-7}\ \Omega$m, then value of R is :

If $50$ Vernier divisions are equal to $49$ main scale divisions of a traveling microscope and one smallest reading of main scale is $0.5\ mm$, the Vernier constant of traveling microscope is

In an experiment to measure the focal length $(f)$ of a convex lens, the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y$-$x$ plot is shown in figure.

The focal length of the lens is ________ $cm$.

[Figure: y–x graph with y (cm) and x (cm) axes marked 10 to 40; data points A, B, C, D, E lie on a downward-sloping curve/line, with point C near (20, 20)]

The resistance per centimeter of a meter bridge wire is $r$, with $X\ \Omega$ resistance in left gap. Balancing length from left end is at 40 cm with $25\ \Omega$ resistance in right gap. Now the wire is replaced by another wire of $2r$ resistance per centimeter. The new balancing length for same settings will be at