An air bubble of radius \(0 .1\, cm\) is in a liquid having surface tension \(0.06\, N/m\) and density \(10^3\, kg/m^3\). The pressure inside the bubble is \(1100\, Nm^{-2}\) greater than the atmospheric pressure. At ....... \(m\) depth is the bubble below the surface of the liquid ? \((g\, = 9.8\, ms^{- 2})\)

A solid metallic cube having total surface area \(24\;m ^{2}\) is uniformly heated. If its temperature is increased by \(10\,^{\circ} C\), calculate the increase in volume of the cube \(\left(\right.\) Given \(\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)\)

A stream of a positively charged particles having \(\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }\) and velocity \(\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s\) is deflected by an electric field \(1.8 \hat{ j } kV / m\). The electric field exists in a region of \(10 cm\) along \(x\) direction. Due to the electric field, the deflection of the charge particles in the \(y\) direction is \(...........mm\)

Resistance of a wire at \(0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}\) and \(t^{\circ} \mathrm{C}\) is found to be \(10 \Omega, 10.2 \Omega\) and \(10.95 \Omega\) respectively. The temperature \(t\) in Kelvin scale is _______.

Three masses \(M =100\,kg , m _{1}=10\,kg\) and \(m_{2}=20\,kg\) are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. \(A\) force \(F\) is applied on the system so that the mass \(m_{2}\) moves upward with an acceleration of \(2\,ms ^{-2}\). The value of \(F\) is \(......N\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

A body starts falling freely from height \(\mathrm{H}\) hits an inclined plane in its path at height \(\mathrm{h}\). As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of \(\frac{\mathrm{H}}{\mathrm{h}}\) for which the body will take the maximum time to reach the ground is _______.

The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1\) \(\mathrm{m}\) is placed in air. The magnetic field at the centre of the loop is \(\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}\). The value of \(\mathrm{X}\) is _______.

Two identical spherical balls of mass \(M\) and radius \(R\) each are stuck on two ends of a rod of length \(2R\) and mass \(M\) (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

From a tower of height \(H\), a particle is thrown vertically upwards with a speed \( u\). The time taken by the particle, to hit the ground, is \(n\) times that taken by it to reach the highest point of its path. The relation between \(H, u\) and \(n\) is:

Two slabs with square cross section of different materials \((1,2)\) with equal sides \((l)\) and thickness \(\mathrm{d}_1\) and \(\mathrm{d}_2\) such that \(\mathrm{d}_2=2 \mathrm{~d}_1\) and \(l \gt \mathrm{d}_2\). Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is \(\theta_2=2 \theta_1\). If the shear moduli of material 1 is \(4 \times 10^9 \mathrm{~N} / \mathrm{m}^2\), then shear moduli of material 2 is \(\mathrm{x} \times 10^9 \mathrm{~N} / \mathrm{m}^2\), where value of \(x\) is ________.

Five charges \(+q,+5 q,-2 q,+3 q\) and \(-4 q\) are situated as shown in the figure. The electric flux due to this configuration through the surface \(S\) is _______.

The energy released if hydrogen atoms are combined to form \(^{4}_{2}\text{He}\) is __________ MeV. (Take binding energies per nucleon of \(^{2}_{1}\text{H}\) and \(^{4}_{2}\text{He}\) as \(1.1\) MeV and \(7.2\) MeV, respectively)