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 $$0.1\mathrm{mm}$$. One main scale division is equal to ________ mm.

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 $$0.04\mathrm{mm}$$ then how many main scale divisions are there in $$1\mathrm{cm}$$ ?

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

Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} LIST I LIST II A. Torque I. $$\left[M^1{L}^1{T}^{-2}{A}^{-2}\right]$$ B. Magnetic field II. $$\left[L^2{A}^1\right]$$ C. Magnetic moment III. $$\left[M^1{T}^{-2}{A}^{-1}\right]$$ D. Permeability of free space IV. $$\left[M^1{L}^2{T}^{-2}\right]$$ Choose the correct answer from the options given below:

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

If the refractive index of the material of a prism is $$\cot \left(\frac{A}{2}\right)$$, where $$A$$ is the angle of prism then the angle of minimum deviation will be

Identify the physical quantity that cannot be measured using spherometer :

A convex lens of focal length $$40\mathrm{cm}$$ forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length $$20\mathrm{cm}$$. The photoelectric current now is :

The refractive index of a prism with apex angle $$A$$ is $$\cot A/2$$. The angle of minimum deviation is :

A convex mirror of radius of curvature $$30\mathrm{cm}$$ forms an image that is half the size of the object. The object distance is :

A biconvex lens of refractive index 1.5 has a focal length of $$20\mathrm{cm}$$ in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

If the distance between object and its two times magnified virtual image produced by a curved mirror is $$15\mathrm{cm}$$, the focal length of the mirror must be:

The following figure represents two biconvex lenses $$L_1$$ and $$L_2$$ having focal length $$10\mathrm{cm}$$ and $$15\mathrm{cm}$$ respectively. The distance between $$L_1$$ & $$L_2$$ is :

Given below are two statements : Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side. Statement (II) : Concave lens always forms a virtual and erect image. In the light of the above statements, choose the correct answer from the options given below :

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $$25\mathrm{D}$$. Focal length of each of the convex lens 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:

The position of the image formed by the combination of lenses is :

Critical angle of incidence for a pair of optical media is $$45^{\circ }$$. The refractive indices of first and second media are in the ratio:

For the thin convex lens, the radii of curvature are at $$15\mathrm{cm}$$ and $$30\mathrm{cm}$$ respectively. The focal length the lens is $$20\mathrm{cm}$$. The refractive index of the material is :