A thin prism \(P_1\) with an angle \(6^{\circ}\) and made of glass of refractive index \(1.54\) is combined with another prism \(P _2\) made from glass of refractive index \(1.72\) to produce dispersion without average deviation. The angle of prism \(P_2\) is \(........{}^{\circ}\)

Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The density of the copper \(\left({ }_{29}^{64} \mathrm{Cu}\right)\) nucleus is greater than that of the carbon \(\left({ }_6^{12} \mathrm{C}\right)\) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to \(\mathrm{A}^{1 / 3}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) is

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are \(B_1\) and \(B_2\) respectively, then the ratio \(\dfrac{B_1}{B_2}\) is _______.

Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau  = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be

A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is .............

A faulty thermometer reads \(5^{\circ} C\) in melting ice and \(95^{\circ} C\) in steam. The correct temperature on absolute scale will be. \(.........K\) when the faulty thermometer reads \(41^{\circ} C\).

A force of \(40\, N\) acts on a point \(B\) at the end of an \(L-\) shaped object, as shown in the figure. The angle \(\theta\) that will produce maximum moment of the force about point \(A\) is given by

In a series \(LCR\) circuit, the inductance, capacitance and resistance are \(L =100\, mH , C =100 \mu F\) and \(R =\) \(10 \Omega\) respectively. They are connected to an \(AC\) source of voltage \(220\, V\) and frequency of \(50\, Hz\). The approximate value of current in the circuit will be.....\(A.\)