The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to \(1.2 \times 10^{-5}\). What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

A liquid of density \(600\) kg/m\(^3\) flowing steadily in a tube of varying cross-section. The cross-section at a point \(A\) is \(1.0\) cm\(^2\) and that at \(B\) is \(20\) mm\(^2\). Both the points \(A\) and \(B\) are in same horizontal plane, the speed of the liquid at \(A\) is \(10\) cm/s. The difference in pressures at \(A\) and \(B\) points is ________ Pa.

What should be the order of arrangement of de-Broglie wavelength of elelctron \(\left(\lambda_{{e}}\right)\), an \(\alpha-\) particle \(\left(\lambda_{\alpha}\right)\) and proton \(\left(\lambda_{p}\right)\) given that all have the same kinetic energy ?

Given below are two statements: Statement \(I:\) Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement \(II:\) Acceleration due to earth's gravity is same at a height ' \(h\) ' and depth ' \(d\) ' from earth's surface, if \(h = d\). In the light of above statements, choose the most appropriate answer form the options given below

Given below are two statements: Statement \(I:\) For diamagnetic substance \(-1 \leq \chi < 0\), where \(\chi\) is the magneticsusceptibility. Statement \(II:\) Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field. In the light of the above statements, choose the correct answer from the options given below.

A particle of mass \(m\) with an initial velocity \(u\hat i\) collides perfectly elastically with a mass \(3m\) at rest. It moves with a velocity \(v\hat j\) after collision, then, \(v\) is given by

A piece of wood from a recently cut tree shows \(20\,decays\) per minute. A wooden piece of same size placed in a museum ( obtained from a tree cut many years back) shows \(2\,decays\) per minute. If half life of \(C^{14}\) is \(5730\, years\), then age of the wooden piece placed in the museum is approximately ........... \(years\)

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

One \(kg\) of water, at \(20\,^oC\), is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of \(20\, \Omega \). The rms voltage in the mains is \(200\, V\). Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to.......... \(\min\) [Specific heat of water \(= 4200\, J/kg\, ^oC\)), Latent heat of water \(= 2260\, k\,J/kg\)]

A body of mass \(m\) is projected with velocity \(\lambda v_{e}\) in vertically upward direction from the surface of the earth into space. It is given that \(v _{ e }\) is escape velocity and \(\lambda<1\). If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be. ( \(R\) : radius of earth)

In a hydrogen atom the electron makes a transition from \(( n +1)^{\text {th }}\) level to the \(n ^{\text {th }}\) level. If \(n>>1,\) the frequency of radiation emitted is proportional to

Student \(A\) and Student \(B\) used two screw gauges of equal pitch and \(100\) equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is \(0.322\, {cm}\). The absolute value of the difference between the final circular scale readings observed by the students \(A\) and \(B\) is .... . [Figure shows position of reference \('O'\) when jaws of screw gauge are closed] Given pitch \(=0.1 \,{cm}\).