Find out the surface charge density at the intersection of point \(x =3\, m\) plane and \(x\) -axis, in the region of uniform line charge of \(8\, nC / m\) lying along the \(z\) -axis in free space.

Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \( x_p(t)=at+bt^2 \) and \(x_Q(t)= ft- t^2\). At what time do the cars have the same velocity \(?\) 

A thin uniform bar of length \(L\) and mass \(8\,m\) lies on a smooth horizontal table. Two point masses \(m\) and \(2\,m\) moving in the same horizontal plane from opposite sides of the bar with speeds \(2v\) and \(v\) respectively. The masses stick to the bar after collision at a distance \(\frac{L}{3}\) and \(\frac{L}{6}\) respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be

The velocity of upper layer of water in a river is \(36 kmh ^{-1}\). Shearing stress between horizontal layers of water is \(10^{-3} Nm ^{-2}\). Depth of the river is \(m\). (Co-efficiency of viscosity of water is \(10^{-2} \,Pa . s\) )

A bicycle tyre is filled with air having pressure of \(270\,kPa\) at \(27^{\circ}\,C\). The approximate pressure of the air in the tyre when the temperature increases to \(36^{\circ}\,C\) is \(............kPa\)

A spherical body of mass \(2\,kg\) starting from rest acquires a kinetic energy of \(10000\,J\) at the end of \(5^{\text {th }}\) second. The force acted on the body is \(.....N\)

Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be _______.

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range \(30\) to \(170\). Reason \(R\) : Nuclear force is short ranged. In the light of the above statements, choose the correct answer from the options given below on

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm , respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be _______.

A body rotating with an angular speed of \(600\, {rpm}\) is uniformly accelerated to \(1800 \,{rpm}\) in \(10\; sec\). The number of rotations made in the process is ..... .

In a scries \(LR\) circuit, power of \(400\, W\) is dissipated from a source of \(250\, V , 50\, Hz\). The power factor of the circuit is \(0.8 .\) In order to bring the power factor to unity, a capacitor of value \(C\) is added in series to the \(L\) and \(R\). Taking the value of \(C\) as \(\left(\frac{ n }{3 \pi}\right) \mu F ,\) then value of \(n\) is\(......\)