The distance travelled by a particle is related to time \(t\) as \(x =4 t ^2\). The velocity of the particle at \(t =\) \(5 s\) is \(.........ms^{-1}\)

A smooth wire of length \(2\pi r\) is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \(\omega\) about the vertical diameter \(AB\), as shown in figure, the bead is at rest with respect to the circular ring at position \(P\) as shown. Then the value of \(\omega^2\) is equal to

A man grows into a giant such that his linear dimensions increase by a factor of \(9\). Assuming that his density remains same, the stress in the leg will change by a factor of

A load of mass \(M\,kg\) is suspended from a steel wire of length \(2\,m\) and radius \(1.0\,mm\) in Searle’s apparatus experiment. The increase in length produced in the wire is \(4.0\,mm.\) Now the load is fully immersed in a liquid of relative density \(2\). The relative density of the material of load is \(8\). The new value of increase in length of the steel wire is ........ \(mm\)

A uniform solid cylindrical roller of mass \('m'\) is being pulled on a horizontal surface with force \(F\) parallel to the surface and applied at its centre. If the acceleration of the cylinder is \('a'\) and it is rolling without slipping then the value of \('F'\) is 

A satellite is moving with a constant speed \(v\) in circular orbit around the earth. An object of mass \(‘m’\) is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

As shown in the figure a block of mass \(10\,kg\) lying on a horizontal surface is pulled by a force \(F\) acting at an angle \(30^{\circ}\), with horizontal. For \(\mu_{ s }=0.25\), the block will just start to move for the value of \(F..........\,N\) : \(\left[\right.\) Given \(\left.g =10\,ms ^{-2}\right]\)

If a wave gets refracted into a denser medium, then which of the following is true?

The electric potential at the centre of two concentric half rings of radii \(R_1\) and \(R_2\), having same linear charge density \(\lambda\) is

In the circuit shown below, maximum zener diode current will be \(.....mA\)