Water from a pipe is coming at a rate of \(100\, litres\) per minute. If the radius of the pipe is \(5\, cm\), the Reynolds number for the flow is of the order of : (density of water \(= 1000\, kg/m^3\), coefficient of viscosity of water \(= 1\, mPa\, s\))

The trajectory of a projectile in a vertical plane is \(y =\alpha x -\beta x ^{2},\) where \(\alpha\) and \(\beta\) are constants and \(x \& y\) are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \(\theta\) and the maximum height attained \(H\) are respectively given by :-

Given a charge \(q\), current I and permeability of vacuum \(\mu_0\). Which of the following quantity has the dimension of momentum?

The alternating current is given by \({i}=\left\{\sqrt{42} \sin \left(\frac{2 \pi}{{T}} {t}\right)+10\right\} {A}\) The \(r.m.s.\) value of this current is \({A}\)

Figure shows a part of an electric circuit. The potentials at points \(a , b\) and \(c\) are \(30\,V , 12\,V\) and \(2\,V\) respectively. The current through the \(20 \Omega\) resistor will be \(........\,A\)

A potentiometer \(PQ\) is set up to compare two resistances as shown in the figure. The ameter \(A\) in the circuit reads \(1.0\, A\) when two way key \(K_3\) is open. The balance point is at a length \(l_1\, cm\) from \(P\) when two way key \(K_3\) is plugged in between \(2\) and \(1\) , while the balance point is at a length \(l_2\, cm\) from \(P\) when key \(K_3\) is plugged in between \(3\) and \(1\) . The ratio of two resistances \(\frac{{{R_1}}}{{{R_2}}}\) is found to be

A body is projected at \(t = 0\) with a velocity \(10\,ms^{-1}\) at an angle of \(60^o\) with the horizontal. The radius of curvature of its trajectory at \(t=1\,s\) is \(R.\) Neglecting air resistance and taking acceleration due to gravity \(g = 10\,ms^{-2},\) the radius of \(R\) is   ........ \(m\)

A heavy iron bar, of weight \(\mathrm{W}\) is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is _______.

The mass per unit length of a uniform wire is \(0.135\, g / cm\). A transverse wave of the form \(y =-0.21 \sin ( x +30 t )\) is produced in it, where \(x\) is in meter and \(t\) is in second. Then, the expected value of tension in the wire is \(x \times 10^{-2} N\). Value of \(x\) is . (Round-off to the nearest integer)

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

The equation of current in a purely inductive circuit is \(5 \sin \left(49 \pi t-30^{\circ}\right)\). If the inductance is \(30\,mH\) then the equation for the voltage across the inductor, will be.\(\left\{\right.\) Let \(\left.\pi=\frac{22}{7}\right\}\)