A progressive wave travelling along the positive \(x-\) direction is represented by \(y(x, t) = A\,sin\,\left( {kx - \omega t + \phi } \right)\). Its snapshot at \(t = 0\) is given in the figure For this wave, the phase \(\phi \) is

A wire carrying current \(I\) is bent in the shape \(A\,B\,C\,D\,E\,F\,A\) as shown, where rectangle \(A\,B\,C\,D\,A\) and \(A\,D\,E\,F\,A\) are perpendicular to each other. If the sides of the rectangles are of lengths \(a\) and \(b,\) then the magnitude and direction of magnetic moment of the loop \(A\,B\,C\,D\,E\,F\,A\,\) is

A particle is rotating in a circular path and at any instant its motion can be described as \(\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}\). The angular acceleration of the particle after \(10\) seconds is _______ rad/s\(^2\).

A spherical body of radius \(r\) and density \(\sigma\) falls freely through a viscous liquid having density \(\rho\) and viscosity \(\eta\) and attains a terminal velocity \(v _0\). Estimated maximum error in the quantity \(\eta\) is : (Ignore errors associated with \(\sigma, \rho\) and g , gravitational acceleration)

Two known resistance of \(R \Omega\) and \(2 R \Omega\) and and one unknown resistance \(X \Omega\) are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is \(X \Omega\), then the value of X is _________ \(\Omega\).

The velocity of sound in air is doubled when the temperature is raised from \(0^{\circ} C\) to \(\alpha^{\circ} C\). The value of \(\alpha\) is ________.

In the given circuit the current through Zener Diode is close to.......\(mA\)

In the circuit shown below, maximum zener diode current will be \(.....mA\)

Particle \(A\) of mass \(m _{1}\) moving with velocity \((\sqrt{3} \hat{i}+\hat{j})\, ms ^{-1}\) collides with another particle \(B\) of mass \(m _{2}\) which is at rest initially. Let \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) be the velocities of particles \(A\) and \(B\) after collision respectively. If \(m _{1}=2\, m _{2}\) and after collision \(\overrightarrow{ V }_{1}=(\hat{ i }+\sqrt{3} \hat{ j })\, ms ^{-1},\) the angle between \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) is\(......^o\)

An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be: