A pressure-pump has a horizontal tube of cross-sectional area \(10\,cm ^{2}\) for the outflow of water at a speed of \(20\,m / s\). The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is \(...N\) [given : density of water \(=1000\,kg / m ^{3}\) ]

An iron rod of volume \(10^{-3}\, m ^{3}\) and relative permeability \(1000\) is placed as core in a solenoid with \(10\) \(turns/cm.\) If a current of \(0.5\, A\) is passed through the solenoid, then the magnetic moment of the rod will be\(...........Am^2\)

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is ___________ \(\times 10^{-5} m\).

The mass of proton, neutron and helium nucleus are respectively \(1.0073\,u , 1.0087\,u\) and \(4.0015\,u\). The binding energy of helium nucleus is \(.........\,MeV\)

Two beams, \(A\) and \(B\), of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam \(A\) has maximum intensity ( and beam \(B\) has zero intensity), a rotation of polaroid through \(30 ^o \) makes the two beams appear equally bright. If the initial intensities of the two beams are \(I_A\) and \(I_B\)  respectively, then \(\frac{{{I_A}}}{{{I_B}}}\)=

The potential energy \((U)\) of a diatomic molecule is a function dependent on \(r\) (interatomic distance) as \(U =\frac{\alpha}{ r ^{10}}-\frac{\beta}{ r ^{5}}-3\) where, \(\alpha\) and \(\beta\) are positive constants. The equilibrium distance between two atoms will be \(\left(\frac{2 \alpha}{\beta}\right)^{\frac{a}{b}},\) where a \(=\) ..........

A series \(LR\) circuit connected with an ac source \(E=(25 \sin 1000 t)\  V\) has a power factor of \(\frac{1}{\sqrt{2}}\). If the source of emf is changed to \(E=(20 \sin 2000 t)\ V,\) the new power factor of the circuit will be _______.

An electromagnetic wave travelling in \(x\)-direction is described by field equation \(E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)\). If the electron is restricted to move in \(y\)-direction only with speed of \(1.5 \times 10^6\) m/s then ratio of maximum electric and magnetic forces acting on the electron is _______.

A uniform heavy rod of mass \(20\,kg\). Cross sectional area \(0.4\,m ^{2}\) and length \(20\,m\) is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is \(x \times 10^{-9} m\). The value of \(x\) is (Given. Young's modulus \(Y =2 \times 10^{11} Nm ^{-2}\) અને \(\left.g=10\, ms ^{-2}\right)\)

Two forces having magnitude \(A\) and \(\frac{ A }{2}\) are perpendicular to each other. The magnitude of their resultant is

A source of sound \(S\) is moving with the velocity of \(50\,m/s\) towards a stationary observer. The observer measures the frequency of the sound as \(1000\,Hz.\) What will be the apparent frequency of the source when it is moving away from the observer after crossing him ... \(Hz\) ? (Take velocity of sound in air is \(350\,m/s\) )