Experimental Physics

The graph between $\dfrac1u$ and $\dfrac1v$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5 and its both the surfaces have same radius of curvature R. The value of R will be ______ cm.

(where $u$ = object distance, $v$ = image distance)

In a Vernier Calipers, 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$^{\text{th}}$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 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$^{\text{th}}$ Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be :

In a meter bridge experiment, for measuring unknown resistance 'S', the null point is obtained at a distance 30 cm from the left side as shown at point D. If R is 5.6 kΩ, then the value of unknown resistance 'S' will be ______ Ω.

The one division of main scale of Vernier callipers reads 1 mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2 cm and 6$^{\text{th}}$ Vernier division coincides with a main scale division. The diameter of the bob will be ______ $\times10^{-2}$ cm.

In an experiment to determine the Young's modulus, steel wires of five different lengths (1, 2, 3, 4, and 5 m) but of same cross section (2 mm$^2$) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x\times10^{11}$ Nm$^{-2}$, then the value of $x$ is ______.

In an experiment with a convex lens, The plot of the image distance ($v'$) against the object distance ($\mu'$) measured from the focus gives a curve $v'\mu'=225$. If all the distances are measured in cm. The magnitude of the focal length of the lens is ______ cm.

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, The accuracy in the determination of g is found to be $x$%. The value of $x$ is ______.

A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope ?

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

(A) Screw moves 0.5 mm on main scale in one complete rotation

(B) Total divisions on circular scale = 50

(C) Main scale reading is 2.5 mm

(D) 45$^{\text{th}}$ division of circular scale is in the pitch line

(E) Instrument has 0.03 mm negative error

Then the diameter of wire is :

The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is

Two identical moving coil galvanometers have 10 Ω resistance and full scale deflection at 2 μA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1 mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with $R = 1000$ Ω resistor by using an ideal cell. Which of the following statement(s) is/are correct?

An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is ______.

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?

A steel wire of diameter 0.5 mm and Young’s modulus $2 \times 10^{11}\ \mathrm{N\,m^{-2}}$ carries a load of mass $M$. The length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 kg, the vernier scale division which coincides with a main scale division is __________. Take $g = 10\ \mathrm{m\,s^{-2}}$ and $\pi = 3.2$.

The following observations were taken for determining surface tension T of water by capillary method :

diameter of capillary, $D=1.25\times10^{-2}$ m

rise of water, $h=1.45\times10^{-2}$ m.

Using $g=9.80$ m/s$^2$ and the simplified relation $T=\dfrac{rhg}2\times10^3$ N/m, the possible error in surface tension is closest to :

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii $r_1$ and $r_2$. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be $5\times10^{-4}$ s, the difference in radii, $|r_1-r_2|$ is best given by :

There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers $(C_1)$ has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper $(C_2)$ has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers $C_1$ and $C_2$, respectively, are

In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2\pi\sqrt{\dfrac{7(R-r)}{5g}}$. The values of $R$ and $r$ are measured to be $(60\pm1)$ mm and $(10\pm1)$ mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?

Consider two identical galvanometers and two identical resistors with resistance $R$. If the internal resistance of the galvanometers $R_C<R/2$, which of the following statement(s) about any one of the galvanometers is(are) true?

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45$^{\text{th}}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25$^{\text{th}}$ division coincides with the main scale line ?