A body of mass \(2\, kg\) is driven by an engine delivering a constant 10.Power \(1\, J / s\). The body starts from rest and moves in a straight line. After \(9\) seconds, the body has moved a distance (in \(m )\)

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity \(K _{1}, K _{2},\) and \(K _{3}\), respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at \(100^{\circ} C\) and the ther at \(0^{\circ} C\) (see figure). If the joints of the rod are at  \(70^{\circ} C\) and \(20^{\circ} C\) in steady state and there is no loss of energy from the surface of the rod, the correct relationship between \(K _{1}, K _{2}\) and \(K _{3}\) is 

If \(C\) and \(V\) represent capacity and voltage respectively then what are the dimensions of \(\lambda,\) where \(\frac{ C }{ V }=\lambda ?\)

A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field \( \vec{E} \) is applied, the final tension in the string changes.The final tension in the string, when pendulum attains an equilibrium position is __________ .
(g: acceleration due to gravity)

The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

The fractional change in the magnetic field intensity at a distance \('r'\) from centre on the axis of current carrying coil of radius \('a'\) to the magnetic field intensity at the centre of the same coil is : (Take \(r << a )\)

A letter \('A'\) is constructed of a uniform wire with resistance \(1.0\,\Omega \) per \(cm\) , The sides of the letter are \(20\, cm\) and the cross piece in the middle is \(10\, cm\) long. The apex angle is \(60\) . The resistance between the ends of the legs is close to ................ \(\Omega\)

A magnet hung at \(45^{\circ}\) with magnetic meridian makes an angle of \(60^{\circ}\) with the horizontal. The actual value of the angle of dip is.

Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is _______.

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where \(\lambda\) is the decay constant)

A coil has an inductance of \(2 H\) and resistance of \(4\,\Omega\). A \(10\,V\) is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be \(..........\times 10^{-2} J\)