A child stands on the edge of the cliff \(10\,m\) above the ground and throws a stone horizontally with an initial speed of \(5\,ms ^{-1}\). Neglecting the air resistance, the speed with which the stone hits the ground will be \(..........ms ^{-1}\) (given, \(g =10\,ms ^{-2}\))

A \(30\) cm long solenoid has \(10\) turns per cm and area of \(5\) cm\(^2\). The current through the solenoid coil varies from \(2\) A to \(4\) A in \(3.14\) s. The e.m.f. induced in the coil is \(\alpha\times 10^{-5}\) V. The value \(\alpha\) is ________.

Consider two identical metallic spheres of radius \(R\) each having charge \(Q\) and mass \(m\). Their centers have an initial separation of \(4 R\). Both the spheres are given an initial speed of \(u\) towards each other. The minimum value of \(u\), so that they can just touch each other is:
(Take \(k=\frac{1}{4 \pi \epsilon_0}\) and assume \(k Q^2>G m^2\) where G is the Gravitational constant)

Diameter of the objective lens of a telescope is \(250\, cm\). For light of wavelength \(600\, nm\). Coming from a distant object, the limit of resolution of the telescope is close to

A capacitor of capacitance \(150.0\,\mu F\) is connected to an alternating source of \(emf\) given by \(E =36\) \(\sin (120 \pi t ) V\). The maximum value of current in the circuit is approximately equal to \(......\,A\)

The induced \(emf\) can be produced in a coil by \(A.\) moving the coil with uniform speed inside magnetic field \(B.\) moving the coil with non-uniform speed inside uniform magnetic field \(C.\) rotating the coil inside the uniform magnetic field \(D.\) changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below:

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \(4^{\text {th}}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and \(5^{\text {th}}\) division of vernier scale coincides with a main scale division. Measured length of cylinder is ___________ mm. (Least count of Vernier calliper \(= 0.1\ mm\))

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media \(A\) and \(B\) are \(2.4 \times 10^8 m / s\) and \(2.7 \times 10^8 m / s\) respectively, then the value of critical angle is :

Two ions having same mass have charges in the ratio \(1: 2\). They are projected normally in a uniform magnetic field with their speeds in the ratio \(2: 3\). The ratio of the radii of their circular trajectories is -

A hole is drilled in a metal sheet. At \(27^{\circ} C\), the diameter of hole is 5 cm . When the sheet is heated to \(177^{\circ} C\), the change in the diameter of hole is \(d \times 10^{-3} cm\). The value of \(d\) will be ________ , if coefficient of linear expansion of the metal is \(1.6 \times 10^{-5} /{ }^{\circ} C\)

A body of mass \(2\,kg\) is initially at rest. It starts moving unidirectionally under the influence of a source of constant 10.Power P. Its displacement in \(4\,s\) is \(\frac{1}{3} \alpha^2 \sqrt{ P } m\). The value of \(\alpha\) will be \(.............\)