In the given figure of meter bridge experiment, the balancing length \(AC\) corresponding to null deflection of the galvanometer is \(40\,cm\). The balancing length, if the radius of the wire \(AB\) is doubled, will be \(....cm\)

If two charges \(q _1\) and \(q _2\) are separated with distance ' \(d\) ' and placed in a medium of dielectric constant \(K\). What will be the equivalent distance between charges in air for the same electrostatic force?

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 \(1 \mathrm{~cm}\) ?

For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 \(\Omega\) is same when both the cells are connected either in parallel or in series. The value of internal resistance r is ___________ \(\Omega\).

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and Rotational Equilibrium is :

There is a small source of light at some depth below the surface of water (refractive index \(=\frac{4}{3}\) ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly)...........\(\%\) [Use the fact that surface area of a spherical cap of height \(\mathrm{h}\) and radius of curvature \(\mathrm{r} \text { is } 2 \pi \mathrm{rh}]\)

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is \((a\,<\,<\,A)\)

Two identical thin metal plates has charge \(q _{1}\) and \(q _{2}\) respectively such that \(q _{1}> q _{2}\). The plates were brought close to each other to form a parallel plate capacitor of capacitance \(C\). The potential difference between them is.

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is :

Two simple pendulums having lengths \(l_1\) and \(l_2\) with negligible string mass undergo angular displacements \(\theta_1\) and \(\theta_2\), from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Two wires \(W_1\) and \(W_2\) have the same radius \(r\) and respective densities \({\rho _1}\) and \({\rho _2}\) such that \({\rho _2} = 4{\rho _1}\). They are joined together at the point \(O\), as  shown in the figure. The combination is used as a sonometer wire and kept under tension \(T\). The point \(O\) is midway between the two bridges. When a stationary waves is set up in the composite wire, the joint is found to be a node. The ratio of the number of an tin odes formed in \(W_1\) to \(W_2\) is

In young's double slit experiment, the fringe width is \(12\,mm\). If the entire arrangement is placed in water of refractive index \(\frac{4}{3}\), then the fringe width becomes \((in\,mm)\)

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are \(10^{15}\text{ atoms/cm}^3\) and \(10^{18}\text{ atoms/cm}^3\), respectively. Which one of the following statements is true ?