A solid body of constant heat capacity \(1\ J/^o C\) is being heated by keeping it in contact with reservoirs in two ways : \((i)\) Sequentially keeping in contact with \(2\) reservoirs such that each reservoir supplies same amount of heat. \((ii)\) Sequentially keeping in contact with \(8\) reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature \(100^o C\) to final temperature \(200^o C\). Entropy change of the body in the two cases respectively is :

Velocity \((v)\) and acceleration \((a)\) in two systems of units \(1\) and \(2\) are related as \(V _{2}=\frac{ n }{ m ^{2}} v _{1}\) and \(a_{2}=\frac{a_{1}}{m n}\) respectively. Here \(m\) and \(n\) are constants. The relations for distance and time in two systems respectively are

The vertical component of the earth's magnetic field is \(6 \times 10^{-5} T\) at any place where the angle of dip is \(37^{\circ}\). The earth's resultant magnetic field at that place will be \(\left(\right.\) Given \(\left.\tan 37^{\circ}=\frac{3}{4}\right)\)

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

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section \(8.0\times10^{-3}\, m^2\) . Initially the gas is at \(300\, K\) and occupies a volume of \(2.4\times10^{-3}\, m^3\) and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by \(0.1\, m\). The force constant of the spring is \(8000\, N/m\) and the atmospheric pressure is \(1.0\times10^5\, N/m^2\) . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater . The heat capacity of the heater coil is also negligible)

Two simple harmonic motion, are represented by the equations \({y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)\) \(y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)\) Ratio of amplitude of \({y}_{1}\) to \({y}_{2}={x}: 1\). The value of \({x}\) is ...... .

A simple pendulum of mass \('m',\) length \('I'\) and charge \('+q'\) suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be -

The current \(i\) in the network is.....\(A\)

Two identical small bar magnets each of dipole moment \(3\sqrt{5}\) J/T are placed at a center to center separation of \(10\) cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is \(\alpha \times 10^{-3}\) T. The value of \(\alpha\) is ______.
(\(\mu_0=4\pi \times 10^{-7}\) Tm/A)

The critical angle for a denser-rarer interface is \(45^{\circ}\). The speed of light in rarer medium is \(3 \times 10^8\) ms. The speed of light in the denser medium is:

A satellite is revolving in a circular orbit at a height \(h\) from the earth surface, such that \(h < < R\) where \(R\) is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is