Two coils, \(X\) and \(Y\), are kept in close vicinity of each other. When a varying current, \(I(t)\), flows through coil \(X\), the induced emf \((V(t))\) in coil \(Y\), varies in the manner shown here. The variation of \(I(t)\); with time, can then be represented by the graph labelled as graph

\(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\).

A current carrying circular loop of radius \(2\) cm with unit normal \(\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}\) is placed in a magnetic field, \(\vec{B} = B_0(3\hat{i}+2\hat{k})\). If \(B_0 = 4\times 10^{-3}\) T and current \(I=100\sqrt{2}\) A, the torque experienced by the loop is ________ Wb·A. (\(\pi=3.14\))

\(M\) grams of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(200\; \mathrm{g}\) of ice at its melting point in a thermally insulated container. If it produces liquid water at \(40^{\circ} \mathrm{C}\) [heat of vaporization of water is \(540 \;cal/\mathrm{g}\) and heat of fusion of ice is \(80 \;\text { cal/g }]\) the value of \(\mathrm{M}\) is

In an experiment to determine the Young's modulus, steel wires of five different lengths \((1,2,3,4\) and \(5\,m )\) but of same cross section \(\left(2\,mm ^{2}\right)\) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is \(x \times 10^{11}\,Nm ^{-2}\), then the value of \(x\) is

A soap bubble of surface tension \(0.04 N / m\) is blown to a diameter of 7 cm . If \((15000- x ) \mu J\) of work is done in blowing it further to make its diameter 14 cm , then the value of x is _________ .\((\pi=22 / 7)\)

A circular disc of mass \(M\) and radius \(R\) is rotating about its axis with angular speed \(\omega_{1}\) If another stationary disc having radius \(\frac{ R }{2}\) and same mass \(M\) is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed \(\omega_{2}\). The energy lost in the process is \(p \%\) of the initial energy. Value of \(p\) is

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 \(......\,A\)

A letter \('A'\) is constructed of a uniform wire with resistance \(1.0\,\Omega \) per \(cm\) , The sides of the letter are \(20\, cm\) and the cross piece in the middle is \(10\, cm\) long. The apex angle is \(60\) . The resistance between the ends of the legs is close to ................ \(\Omega\)

A particle of mass \(m\) is moving along the side of a square of side '\(a\)', with a uniform speed \(v\) in the \(x-y\) plane as shown in the figure Which of the following statement is false for the angular momentum \(\vec L\) about the origin ?