In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of \(8 \mathrm{~A} / \mathrm{s}\). At an instant when R is \(12 \Omega\), the value of the current in the circuit will be ______ A.

A projectile is launched at an angle ' \(\alpha\) ' with the horizontal with a velocity \(20 \; ms ^{-1}\). After \(10 s\), its inclination with horizontal is ' \(\beta\) '. The value of \(\tan \beta\) will be : \(\left( g =10 \; ms ^{-2}\right)\)

If the time period \(t\) of the oscillation of a drop of liquid of density \(d\), radius \(r\), vibrating under surface tension \(s\) is given by the formula \(t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} \) . It is observed that the time period is directly proportional to \(\sqrt {\frac{d}{s}} \) . The value of \(b\) should therefore be

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

A tuning fork of frequency \(340\,Hz\) resonates in the fundamental mode with an air column of length \(125\,cm\) in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ \(cm\) (Velocity of sound in air is \(340\,ms ^{-1}\) )

An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

One end of a massless spring of spring constant \(k\) and natural length \(l_{0}\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(\omega\) about an axis passing through fixed end, then the elongation of the spring will be

Magnetic field in a plane electromagnetic wave is given by  \(\vec B = {B_0}\,\sin \,\left( {kx + \omega t} \right)\hat jT\)  Expression for corresponding electric field will be Where \(c\) is speed of light

Three charges +2q. +3q and -4q are situated at (0,-3a), (2a, 0) and (-2a,0) respectively in the xy plane. The resultant dipole moment about origin is _________

A transverse harmonic wave on a string is given by \(y(x, t)=5 \sin (6 t+0.003 x)\) where \(x\) and \(y\) are in \(cm\) and \(t\) in \(sec\). The wave velocity is \(...........\,ms ^{-1}\).

Projectiles \(A\) and \(B\) are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection \(v_A: v_B\) is _______.

A coil of circular cross-section having \(1000\, turns\) and \(4\, cm^2\) face area is placed with its axis parallel to a magnetic field which decreases by \(10^{-2}\, Wb\, m^{-2}\) in \(0.01\, s\). The \(e.m.f.\) induced in the coil is....\(mV\)