The initial mass of a rocket is \(1000\, {kg} .\) Calculate at what rate the fuel (In \({kg} {s}^{-1}\)) should be burnt so that the rocket is given an acceleration of \(20 \,{ms}^{-2}\). The gases come out at a relative speed of \(500\, {ms}^{-1}\) with respect to the rocket : [Use \( g = 10\, {m} / {s}^{2}\) ]

A tennis ball is dropped on to the floor from a height of \(9.8\,m\). It rebounds to a height \(5.0\,m\). Ball comes in contact with the floor for \(0.2\,s\). The average acceleration during contact is \(..........ms ^{-2}\). [Given \(g =10\,ms ^{-2}\) ]

A resistor develops \(300 \,J\) of thermal energy in \(15 \,s\), when a current of \(2\, A\) is passed through it. If the current increases to \(3 \,A\), the energy developed in \(10\,\,s\)  is........\(J.\)

To get output ‘\(1\)’ at \(R\), for the given logic gate circuit the input values must be

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio \(3: 2\). The ratio of their nuclear sizes will be \(\left(\frac{x}{3}\right)^{\frac{1}{3}}\). The value of ' \(x\) ' is :

A thin lens made of glass (refractive index \(= 1.5\)) of focal length \(f=16\; \mathrm{cm}\) is immersed in a liquid of refractive index \(1.42 .\) If its focal length in liquid is \(f_{l},\) then the ratio \(f_{l} /f\) is closest to the integer

An electric bulb rated as \(200\, {W}\) at \(100 \,{V}\) is used in a circuit having \(200\, {V}\) supply. The resistance \('R'\) that must be put in series with the bulb so that the bulb delivers the same power is \(.....\,\Omega\)

In an experiment with a closed organ pipe, it is filled with water by \(\left(\frac{1}{5}\right)\) th of its volume. The frequency of the fundamental note will change by

A balloon has mass of \(10\,g\) in air. The air escapes from the balloon at a uniform rate with velocity \(4.5\,cm / s\). If the balloon shrinks in \(5\,s\) completely. Then, the average force acting on that balloon will be (in dyne).

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is:-

Two stars of masses \(m\) and \(2\, m\) at a distance \(d\) rotate about their common centre of mass in free space. The period of revolution is

Given below are two statements Statement \(I\) : The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle Statement \(II\) : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below