When a rubber-band is stretched by a distance \(x\), it exerts restoring force of magnitude  \(F=ax+bx^2\) where \(a\) and \(b\) areconstants. The work done in stretching the unstretched rubber-band by \(L\) is

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________.

A wire of density \(9 \times 10^{-3} \,kg\, cm ^{-3}\) is stretched between two clamps \(1\, m\) apart. The resulting strain in the wire is \(4.9 \times 10^{-4}\). The lowest frequency of the transverse vibrations in the wire is......\(HZ\) (Young's modulus of wire \(Y =9 \times 10^{10}\, Nm ^{-2}\) ), (to the nearest integer),

The voltage drop across \(15\, \Omega\) resistance in the given figure will be \(.....V.\)

A beam of light consisting of two wavelengths \(7000\; \mathring A\) and \(5500 \;\mathring A\) is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is \(2.5\,mm\) and the distance between the plane of slits and the screen is \(150\,cm\). The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is \(n \times 10^{-5}\,m\). The value of \(n\) is .............

In a meter bridge experiment the balance point in obtained if the gaps are closed by \(2\,\Omega\) and \(3\,\Omega\). A shunt of \(x\,\Omega\) is added to \(3\,\Omega\) resistor to shift the balancing point by \(22.5\,cm\). The value of \(X\) is \(................\)

A galvanometer with its coil resistance \(25\,\Omega \) requires a current of  \(1\,mA\)  for its full deflection. In order to construct an ammeter to read up to a current of \(2\,A,\)  the approximate value of the shunt resistance should be

An organ pipe \(40\,cm\) long is open at both ends. The speed of sound in air is \(360\,ms ^{-1}\). The frequency of the second harmonic is \(...........\,Hz\).

The elastic limit of brass is \(379\,MPa.\) .......... \(mm\) should be the minimum diameter of a brass rod if it is to support a \(400\,N\) load without exceeding its elastic limit .

Two cars \(A\) and \(B\) are moving away from each other in opposite directions. Both the cars are moving with a speed of \(20\, ms^{-1}\) with respect to the ground. If an observer in car \(A\) detects a frequency \(2000\, Hz\) of the sound coming from car \(B\), what is the natural frequency of the sound source of car \(B\) ....  \(Hz\) ? (speed of sound in air \(= 340\, ms^{-1}\))