In a transverse wave the distance between a crest and neighbouring trough at the same instant is \(4.0\, cm\) and the distance between a crest and trough at the same place is \(1 .0\, cm\) . The next crest appears at the same place after a time interval of \(0.4\,s\). The maximum speed of the vibrating particles in the medium is

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field \(B_1,\) at its centre when a current \(I\) passes through it.The second wire is bent into a coil with  three identical loops adjacent to each other and produces magnetic field \(B_2\) at the centre of the loops when current \(I/3\) passes through it. The ratio \(B_1 : B_2\) is

The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is \(1 : 4\). What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is __________ m/s.

A particle is projected at an angle of \(30^{\circ}\) from horizontal at a speed of \(60 \mathrm{~m} / \mathrm{s}\). The height traversed by the particle in the first second is \(\mathrm{h}_0\) and height traversed in the last second, before it reaches the maximum height, is \(h_1\). The ratio \(h_0: h_1\) is _________
[Take, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ]

An object of mass ' \(m\) ' initially at rest on a smooth horizontal plane starts moving under the action of force \(F=2 N\). In the process of its linear motion, the angle \(\theta\) (as shown in figure) between the direction of force and horizontal varies as \(\theta= kx\), where \(k\) is a constant and \(x\) is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be \(E =\frac{ n }{ k } \sin \theta\). The value of \(n\) is \(.....\)

\(LCR\) circuit is at resonance for a capacitor \(C\), inductance \(L\) and resistance \(R\). Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now what?

Calculate the time (in \(minutes\)) interval between \(33 \,\%\) decay and \(67\, \%\) decay if half-life of a substance is \(20\, minutes.\)

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \(V ^q\), where \(V\) is the volume of the gas. The value of \(q\) is \(\left( {\gamma = \frac{{{C_P}}}{{{C_V}}}} \right)\)

In the cube of side \(a\) shown in the figure, the vector from the central point of the face \(ABOD\) to the central point of the face \(BEFO\) will be

Critical angle of incidence for a pair of optical media is \(45^{\circ}\). The refractive indices of first and second media are in the ratio _______.

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 \(=\) ..........