A rod of linear mass density ' \(\lambda\) ' and length ' \(L\) ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

A wire of resistance \(R\) is bent to form a square \(ABCD\) as shown in the figure. The effective resistance between \(E\) and \(C\) is ( \(E\) is mid-point of arm \(CD\) )

Two capacitors of capacitances \(C\) and \(2\, C\) are charged to potential differences \(V\) and \(2\, V\), respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is\(.....CV^2\)

Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) is

A Copper \((Cu)\) rod of length \(25\, {cm}\) and cross- sectional area \(3\, {mm}^{2}\) is joined with a similar Aluminium \((Al)\) rod as shown in figure. Find the resistance of the combination between the ends \(A\) and \(B\) (in \({m} \Omega\)) (Take Resistivity of Copper \(=1.7 \times 10^{-8}\, \Omega \,{m}\), Resistivity of Aluminium \(=2.6 \times 10^{-8}\, \Omega \,{m}\) )

A capacitor, \(C_1=6 \mu \mathrm{~F}\) is charged to a potential difference of \(\mathrm{V}_0=5 \mathrm{~V}\) using a 5 V battery. The battery is removed and another capacitor, \(\mathrm{C}_2=12 \mu \mathrm{~F}\) is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges \(\left(q_1\right.\) and \(\left.q_2\right)\) on the capacitors \(C_1\) and \(C_2\) when equilibrium condition is reached.

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below