A gas is compressed adiabatically, which one of the following statement is NOT true.

A force on an object of mass \(100\, g\) is \((10 \hat{i}+5 \hat{j}) N\). The position of that object at \(t=\) \(2 s\) is \((a \hat{i}+b \hat{j}) m\) after starting from rest. The value of \(\frac{a}{b}\) will be..........

A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is :

An electron is moving along \(+x\) direction with a velocity of \(6 \times 10^{6}\, ms ^{-1}\). It enters a region of uniform electric field of \(300 \,V / cm\) pointing along \(+ y\) direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the \(x\) direction will be

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is _______. (Given \(=\) Radius of geo-stationary orbit for earth is \(4.2 \times 10^4 \mathrm{~km}\) )

An object of mass \(m\) is suspended at the end of a massless wire of length \(L\) and area of cross\(-\)section, \(A\). Young modulus of the material of the wire is \(Y\). If the mass is pulled down slightly its frequency of oscillation along the vertical direction is

A ball of mass 100 g is projected with velocity \(20 \mathrm{~m} / \mathrm{s}\) at \(60^{\circ}\) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true\(?\) \((A)\) the mean free path of the molecules decreases. \((B)\) the mean collision time between the molecules decreases. \((C)\) the mean free path remains unchanged. \((D)\) the mean collision time remains unchanged.

A transverse wave travels on a taut steel wire with a velocity of \({v}\) when tension in it is \(2.06 \times 10^{4} \;\mathrm{N} .\) When the tension is changed to \(T\). the velocity changed to \(\frac v2\). The value of \(\mathrm{T}\) is close to