Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is \(1: 4,\) the ratio of their diameters is

A wire of length \(L\) and radius \(r\) is clamped rigidly at one end. When the other end of the wire is pulled by a force \(F\), its length increases by \(5\,cm\). Another wire of the same material of length \(4 L\) and radius \(4\,r\) is pulled by a force \(4\,F\) under same conditions. The increase in length of this wire is \(....cm\).

This question has Statement \(- 1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement \(1\) : The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement \(2\) : A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.

A \(0.07\,{H}\) inductor and a \(12 \,\Omega\) resistor are connected in series to a \(220 \,{V}, 50 \,{Hz}\) ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take \(\pi\) as \(\left.\frac{22}{7}\right]\)

A parallel plate capacitor of capacitance \(1 \mu \mathrm{~F}\) is charged to a potential difference of 20 V . The distance between plates is \(1 \mu \mathrm{~m}\). The energy density between plates of capacitor is _________.

Figure here shows \(P\) and \(Q\) as two equally intense coherent sources emitting radiations of wavelength \(20 \,m\). The separation \(PQ\) is \(5.0 \,m\) and phase of \(P\) is ahead of the phase of \(Q\) by \(90^{0}\). \(A, B \) and \( C\) are three distant points of observation equidistant from the mid-point of \(PQ\). The intensity of radiations at \(A, B, C\)  will bear the ratio

When two sound waves travel in the same direction in a medium, the displacements of a particle located at \('x'\) at time \('t'\) is given by \({y_1} = 0.05\,\cos \,\left( {0.50\,\pi x - 100\,\pi t} \right)\) \({y_2} = 0.05\,\cos \,\left( {0.46\,\pi x - 92\,\pi t} \right)\) then velocity is..... \(m/s\)

The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V _{ Z }=5 V\) and the desired current in load is 5 mA . The unregulated voltage source can supply upto 25 V . Considering the Zener diode can withstand four times of the load current, the value of resistor \(R _{ S }\) (shown in circuit) should be ___________ \(\Omega\).

When a car is approaching the observer, the frequency of horn is \(100 Hz\). After passing the observer, it is \(50\,Hz\). If the observer moves with the car, the frequency will be \(\frac{ x }{3} Hz\) where \(x =.....\)

Two planets \(A\) and \(B\) of equal mass are having their period of revolutions \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 T_{B}\). These planets are revolving in the circular orbits of radii \(I_{A}\) and \(I_{B}\) respectively. Which out of the following would be the correct relationship of their orbits?