A resistor develops \(500\, J\) of thermal energy in \(20 \,s\) when a current of \(1.5\, A\) is passed through it. If the current is increased from \(1.5 \,A\) to \(3\, A\) what will be the energy (in \(J\)) developed in \(20\, s\).

A small block of mass \(100\,g\) is tied to a spring of spring constant \(7.5\,N / m\) and length \(20\, cm\). The other end of spring is fixed at a particular point \(A\). If the block moves in a circular path on a smooth horizontal surface with constant angular velocity \(5\,rad / s\) about point \(A\), then tension in the spring is \(.........\,N\)

\(n\) polarizing sheets are arranged such that each makes an angle \(45^{\circ}\) with the proceeding sheet. An unpolarized light of intensity \(I\) is incident into this arrangement. The output intensity is found to be \(\frac{I}{64}\). The value of \(n\) will be:

At a given point of time the value of displacement of a simple harmonic oscillator is given as \(y = A \cos \left(30^{\circ}\right)\). If amplitude is \(40\,cm\) and kinetic energy at that time is \(200\, J\), the value of force constant is \(1.0 \times 10^{ x }\,Nm ^{-1}\). The value of \(x\) is ......

A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is

A calorimeter of water equivalent \(20\, g\) contains \(180\, g\) of water at \(25^{\circ} C\). '\(m\)' grams of steam at \(100^{\circ} C\) is mixed in it till the temperature of the mixure is \(31^{\circ} C\). The value of \('m'\) is close to (Latent heat of water \(=540\) cal \(g ^{-1}\), specific heat of water \(=1\) cal \(g^{-1}{ }^{\circ} C ^{-1}\) )

A wire \(A\), bent in the shape of an arc of a circle, carrying a current of \(2\, A\) and having radius \(2\, cm\) and another wire \(B ,\) also bent in the shape of arc of a circle, carrying a current of \(3\, A\) and having radius of \(4\, cm ,\) are placed as shown in the figure. The ratio of the magnetic fields due to the wires \(A\) and \(B\) at the common centre \(O\) is

A car is moving with speed of \(150\,km / h\) and after applying the brake it will move \(27\,m\) before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling \(....m\) distance.

Two point charges \(-4 \mu c\) and \(4 \mu c\), constituting an electric dipole, are placed at \((-9,0,0) \mathrm{cm}\) and \((9,0,0) \mathrm{cm}\) in a uniform electric field of strength \(10^4 \mathrm{NC}^{-1}\). The work done on the dipole in rotating it from the equilibrium through \(180^{\circ}\) is :

A potentiometer wire \(AB\) having length \(L\) and resistance \(12\, r\) is joined to a cell \(D\) of \(emf\) \(\varepsilon \) and internal resistance \(r\). A cell \(C\) having \(emf\) \(\varepsilon /2\) and internal resistance \(3r\) is connected. The length \(AJ\) at which the galvanometer as shown in figure shows no deflection is

In the reported figure of earth, the value of acceleration due to gravity is same at point \(A\) and \(C\) but it is smaller than that of its value at point \(B\) (surface of the earth). The value of OA \(: AB\) will be \(x : y .\) The value of \(x\) is \(\ldots \ldots \ldots\)

Conductor wire ABCDE with each \(\operatorname{arm} 10 \mathrm{~cm}\) in length is placed in magnetic field of \(\frac{1}{\sqrt{2}}\) Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of \(10 \mathrm{~cm} / \mathrm{s}\), induced emf between points A and E is _____ mV.