A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is \(\frac{4}{3}\),  and the diver's eyes are \(15\, cm\) below the surface of water. Then the radius of the circle is

A steel wire of length \(3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)\) and a copper wire of length \(4.4\,M\) \(\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)\), both of radius \(1.4\,mm\) are connected end to end. When stretched by a load, the net elongation is found to be \(1.4\,mm\). The load applied, in Newton, will be. (Given \(\pi=\frac{22}{7}\))

In the given arrangement of a doubly inclined plane two blocks of masses \(\mathrm{M}\) and \(\mathrm{m}\) are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is \(0.25\) . The value of \(\mathrm{m}\), for which \(\mathrm{M}=10\) \(\mathrm{kg}\) will move down with an acceleration of \(2 \mathrm{~m} / \mathrm{s}^2\), is _______. (take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) and \(\left.\tan 37^{\circ}=3 / 4\right)\)

For a plane electromagnetic wave, the magnetic field at a point \(x\) and time \(t\) is \(\overrightarrow{ B }( x , t )=\left[1.2 \times 10^{-7} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ k }\right] T\) The instantaneous electric field \(\overrightarrow{ E }\) corresponding to \(\overrightarrow{ B }\) is : (speed of light \(\left.c=3 \times 10^{8} ms ^{-1}\right)\)

Two particles \(A, B\) are moving on two concentric circles of radii \(R_1\) and \(R_2\) with equal angular speed \(\omega \). At \(t = 0,\) their positions and direction of motion are shown in the figure The relative velocity \(\overrightarrow {{V_A}}  - \overrightarrow {{V_B}} \) at \(t = \frac{\pi }{{2\omega }}\) is given by

In the given circuit, the charge on \(4\, \mu F\) capacitor will be.....\(\mu C\)

A plane electromagnetic wave of wavelength \(\lambda \) has an intensity \(I.\)  It is propagating along the positive \(Y-\)  direction. The allowed expressions for the electric and magnetic fields are given by

A bakelite beaker has volume capacity of \(500\, cc\) at \(30^{\circ} C\). When it is partially filled with \(V _{ m }\) volume (at \(30^{\circ}\) ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} C ^{-1}\) and \(\gamma_{(\text {mercury })}=1.5 \times 10^{-4}{ }^{\circ} C ^{-1},\) where \(\gamma\) is the coefficient of volume expansion, then \(V _{ m }(\)in \(cc )\) is close to

Keeping the significant figures in view, the sum of the physical quantities \(52.01 m, 153.2 m\) and 0.123 m is :

A given object takes \(n\) times the time to slide down \(45^{\circ}\) rough inclined plane as it takes the time to slide down an identical perfectly smooth \(45^{\circ}\) inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is _______.