Two cells are connected in opposition as shown. Cell \(\mathrm{E}_1\) is of \(8 \mathrm{~V}\) emf and \(2 \ \Omega\) internal resistance; the cell \(E_2\) is of \(2 \mathrm{~V}\) emf and \(4\ \Omega\) internal resistance. The terminal potential difference of cell \(\mathrm{E}_2\) is _______.

An engine approaches a hill with a constant speed. When it is at a distance of \(0.9\, km\), it blows a whistle whose echo is heard by the driver after \(5\, seconds\). If the speed of sound in air is \(330\, m/s\), then the speed of the engine is .... \(m/s\)

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

A spring mass system (mass \(m\), spring constant \(\mathrm{k}\) and natural length \(l\) ) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity \(\omega,\left(\mathrm{k} > > \mathrm{m} \omega^{2}\right)\) the relative change in the length of the spring is best given by the option

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then \(A.\) The \(r.m.s\). velocity of gas molecules in two vessels will be the same. \(B.\) The ratio of pressure in these vessels will be \(1: 4\) \(C.\) The ratio of pressure will be \(1: 1\) \(D.\) The \(r.m.s.\) velocity of gas molecules in two vessels will be in the ratio of \(1: 4\)

A rod of length \(L\) at room temperature and uniform area of cross section \(A\), is made of a metal having coefficient of linear expansion \(\alpha {/^o}C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by \(\Delta \,TK\). Young’s modulus, \(Y\), for this metal is

Car \(B\) overtakes another car \(A\) at a relative speed of \(40\, ms^{-1}\). How fast will the image of car \({B}\) appear to move in the mirror of focal length \(10\, cm\) fitted in car \({A}\), when the car \({B}\) is \(1.9\, m\) away from the car \({A}\) ? (In \(ms^{-1}\))

Two sitar strings, \(A\)  and \(B,\)  playing the note \('Dha'\)  are slightly out of tune and produce beats and frequency  \(5\,Hz.\)  The tension of the string \(B\) is slightly increased and the beat frequency is found to decrease by  \(3\,Hz\) . If the frequency of \(A\) is \(425\,Hz,\)  the original frequency of \(B\) is  ... \(Hz\)

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of \(\left[M^a L^b T^c\right]\). If \(b=-3\), the value of \(c\) 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 _______.