A machine gun of mass \(10\,kg\) fires \(20\,g\) bullets at the rate of \(180\) bullets per minute with a speed of \(100\,m s ^{-1}\) each. The recoil velocity of the gun is \(.............\,m/s\)

An air bubble of diameter \(6\,mm\) rises steadily through a solution of density \(1750\,kg / m ^3\) at the rate of \(0.35\,cm / s\). The co-efficient of viscosity of the solution (neglect density of air) is \(..........\,Pas\) (given, \(g =10\,ms ^{-2}\))

A transparent cube of side \(d\), made of a material of refractive index \(\mu_2\), is immersed in a liquid of refractive index \(\mu_1(\mu_1 < \mu_2)\). A ray is incident on the face \(AB\) at an angle \(\theta \) (shown in the figure). Total internal reflection takes place at point \(E\) on the face \(BC\). The \(\theta\) must satisfy

A refrigerator consumes an average \(35\, {W}\) power to operate between temperature \(-10^{\circ} {C}\) to \(25^{\circ} {C}\). If there is no loss of energy then how much average heat per second does it transfer? (in \({J} / {s}\))

In the experiment of \(Ohm's law,\) a potential difference of \(5.0\, V\) is applied across the end of a conductor of length \(10.0\, cm\) and diameter of \(5.00\, mm .\) The measured current in the conductor is \(2.00\, A\). The maximum permissible percentage error in the resistivity of the conductor is

A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \; kmh ^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is ...........  \(kmh ^{-1}\)

A block of mass \(10\,kg\) is moving along \(x\)-axis under the action of force \(F=5 x\; N\). The work done by the force in moving the block from \(x =2\,m\) to \(4\,m\) will be ............\(J\).

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is _______.

Two resistors \(2 \Omega\) and \(3 \Omega\) are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY . When an unknown resistor is connected in parallel with \(3 \Omega\) resistor, the null point is shifted by 22.5 cm toward Y . The resistance of unknown resistor is _________ \(\Omega\).

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the \(n^{th}\) orbital will therefore be proportional to

Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below.