A capacitor of capacitance \(50 \; pF\) is charged by \(100 \; V\) source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is \(\dots \; nJ\).

A ring of mass \(M\) and radius \(R\) is rotating about its axis with angular velocity \(\omega \). Two identical bodies each of mass \(m\) are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be

Consider a \(72\, cm\) long wire \(AB\) as shown in the figure. The galvanometer jockey is placed at \(P\) on \(A B\) at a distance \(x cm\) from \(A\). The galvanometer shows zero deflection. The value of \(x,\) to the nearest integer, is ..... \(cm\)

Two identical capacitors \(\mathrm{A}\) and \(\mathrm{B}\), charged to the same potential \(5\; \mathrm{V}\) are connected in two different circuits as shown below at time \(\mathrm{t}=0\) If the charge on capacitors \(A\) and \(B\) at time \(\mathrm{t}=\mathrm{CR}\) is \(\mathrm{Q}_{\mathrm{A}}\) and \(\mathrm{Q}_{\mathrm{B}}\) respectively, then (Here \(e\) is the base of natural logarithm)

In a Young's double slit experiment, two slits are illuminated with a light of wavelength \(800 nm\). The line joining \(A _1 P\) is perpendicular to \(A _1 A _2\) as shown in the figure. If the first minimum is detected at \(P\), the value of slits separation ' \(a\) ' will be \(.........\,mm\) The distance of screen from slits \(D =5\,cm\)

A screw gauge of pitch \(0.5\,mm\) is used to measure the diameter of uniform wire of length \(6.8\,cm\), the main scale reading is \(1.5\,mm\) and circular scale reading is \(7\). The calculated curved surface area of wire to appropriate significant figures is \(......cm^2\) . [Screw gauge has \(50\) divisions on the circular scale]

A current through a wire depends on time as \(i =\alpha_{0} t +\beta t ^{2}\) where \(\alpha_{0}=20 A / s\) and \(\beta=8 As ^{-2} .\) Find the charge crossed through a section of the wire in \(15 \,s\) (in \(C\))

Two cells of emf \(2\, E\) and \(E\) with internal resistance \(r _{1}\) and \(r _{2}\) respectively are connected in series to an external resistor \(R\) (see \(figure\)). The value of \(R ,\) at which the potential difference across the terminals of the first cell becomes zero is

An air bubble of radius \(0 .1\, cm\) is in a liquid having surface tension \(0.06\, N/m\) and density \(10^3\, kg/m^3\). The pressure inside the bubble is \(1100\, Nm^{-2}\) greater than the atmospheric pressure. At ....... \(m\) depth is the bubble below the surface of the liquid ? \((g\, = 9.8\, ms^{- 2})\)

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)

In case of vertical circular motion of a particle by a thread of length \(r\) if the tension in the thread is zero at an angle \(30^{\circ}\) shown in figure, the velocity at the bottom point (A) of the circular path is ( \(g =\) gravitational acceleration)

In an experiment with Vernier callipers of least count \(0.1\,mm\), when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and \(6^{\text {th }}\) division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between \(3.2\,cm\) and \(3.3\,cm\) marks, and \(4^{\text {th }}\) division of vernier scale coincides with the main scale division. The diameter of bob is measured as \(.......\,cm\)