A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity \(\omega\). A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If \(E\) be the initial Kinetic energy of the system, then final Kinetic energy will be \(\frac{E}{x}\).The value of \(x\) is \(....\)

A prism of refractive index \(n_{1}\) and another prism of refractive index \(n_{2}\) are stuck together (as shown in the figure). \(n_{1}\) and \(n_{2}\) depend on \(\lambda\), the wavelength of light, according to the relation \({n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text { and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}\) The wavelength for which rays incident at any angle on the interface \(B C\) pass through without bending at that interface will be \(....\,nm.\)

From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is ______ \(\mu\)F.
(take \(C_1=C_2=C_3=1\) \(\mu\)F and \(C_4=2\) \(\mu\)F.)

A planet revolving in elliptical orbit has \((A)\) a constant velocity of revolution. \((B)\) has the least velocity when it is nearest to the sun. \((C)\) its areal velocity is directly proportional to its velocity. \((D)\) areal velocity is inversely proportional to its velocity. \((E)\) to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below

A circular coil of radius \(8.0 \,{cm}\) and \(20\) turns is rotated about its vertical diameter with an angular speed of \(50\, {rad} {s}^{-1}\) in a uniform horizontal magnetic field of \(3.0 \times 10^{-2}\, {T}\). The maximum \(emf\) induced the coil will be \(\ldots \ldots \ldots \times 10^{-2}\) \(volt\) (rounded off to the nearest integer)

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility \(\left.\chi_{\mathrm{mg}}=1.2 \times 10^{-5}\right)\) is :

As shown in the figure, the voltmeter reads \(2\,V\) across \(5\,\Omega\) resistor. The resistance of the voltmeter is \(.......\,\Omega\).

Two cells of same emf but different internal resistances \(I_{1}\) and \(I_{2}\) are connected in series with a resistance \(R\). The value of resistance \(R\), for which the potential difference across second cell is zero, is

A bimetallic strip consists of metals \(A\) and \(B\). It is mounted rigidly as shown. The metal \(A\) has higher coefficient of expansion compared to that of metal \(B\). When the bimetallic strip is placed in a cold both, it will :

In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is \(\frac{1}{8} ^{th}\) of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \(R_1=2 \pi\  \mathrm{m}\) and \(R_2=4 \pi\  \mathrm{m}\) carrying current \(I=4 \mathrm{~A}\) as per figure given below is \(\alpha \times 10^{-7} \mathrm{~T}\). The value of \(\alpha\) is___________ (Centre \(\mathrm{O}\) is common for all segments)

Three rods of Copper, Brass and Steel are welded together to form a \(Y\) shaped structure. Area of cross - section of each rod \(= 4\ cm^2\) . End of copper rod is maintained at \(100^o C \) where as ends ofbrass and steel are kept at \(0^o C\). Lengths of the copper, brass and steel rods are \(46, 13\) and \(12\ cms\) respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are \(0.92, 0.26\) and \(0.12\ CGS\) units respectively. Rate ofheat flow through copper rod is ....... \(cal\, s^{-1}\)