When two soap bubbles of radii \(a\) and \(b ( b > a )\) coalesce, the radius of curvature of common surface is

A big drop is formed by coalescing \(1000\) small droplets of water. The ratio of surface energy of \(1000\) droplets to that of energy of big drop is \(\frac{10}{x}\). The value of \(x\) is _______.

A vertical electric field of magnitude \(4.9 \times 10^{5} N / C\) just prevents a water droplet of a mass \(0.1\, g\) from falling. The value of charge on the droplet will be  ........ \(\times 10^{-9} \;C\) \(\left(\right.\) Given \(\left.g =9.8 m / s ^{2}\right)\)

Two metallic blocks \(M_{1}\) and \(M_{2}\) of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of \(M _{2}\) is \(K\) then the thermal conductivity of \(M _{1}\) will be ]...............\(K\) [Assume steady state heat conduction]

An object is projected with kinetic energy K from a point A at an angle \(60^{\circ}\) with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :

A cyclist starts from the point \(P\) of a circular ground of radius \(2 \mathrm{~km}\) and travels along its circumference to the point \(\mathrm{S}\). The displacement of a cyclist is _______.

A particle of mass \(m\) moving with velocity \(v\) collides with a stationary particle of mass \(2m\). After collision, they stick together and continue to move together with velocity ........

An \(\alpha\) particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be.

If \(1000\) droplets of water of surface tension \(0.07\,N / m\). having same radius \(1\,mm\) each, combine to from a single drop. In the process the released surface energy is \(\left(\text { Take } \pi=\frac{22}{7}\right)\)

Magnitude of magnetic field (in \(SI\) units) at the centre of a hexagonal shape coil of side \(10\, cm\), \(50\) turns and carrying current \(I\) (Ampere) in units of \(\frac{\mu_{0} I}{\pi}\) is

A thermodynamic system is taken from an original state \(A\) to an intermediate state \(B\) by a linear process as shown in the figure. It's volume is then reduced to the original value from \(B\) to \(C\) by an isobaric process. The total work done by the gas from \(A\) to \(B\) and \(B\) to \(C\) would be :

A boy is rolling a \(0.5\, kg\) ball on the frictionless floor with the speed of \(20\, ms ^{-1}\). The ball gets deflected by an obstacle on the way. After deflection it moves with \(5 \%\) of its initial kinetic energy. What is the speed of the ball now ? (in \(ms ^{-1}\))

An \(HCl\) molecule has rotational, translational and vibrational motions. If the \(rms\) velocity of \(HCl\) molecules in its gaseous phase is \(\bar v ,\,m\) is its mass and \(k_B\) is Boltzmann constant, then its temperature will be