Water of mass \(m\) gram is slowly heated to increase the temperature from \(T_1\) to \(T_2\) The change in entropy of the water, given specific heat of water is \(1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\), is :

In an engine the piston undergoes vertical simple harmonic motion with amplitude \(7\, cm\) . A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to ...... \(Hz\)

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ___________ cm.

A charge particle of \(2\,\mu\,C\) accelerated by a potential difference of \(100\,V\) enters a region of uniform magnetic field of magnitude \(4\,m\,T\) at right angle to the direction of field. The charge particle completes semicircle of radius \(3\,cm\) inside magnetic field. The mass of the charge particle is \(........\times 10^{-18}\,kg\).

Two light beams fall on a transparent material block at point 1 and 2 with angle \(\theta_1\) and \(\theta_{2^{\prime}}\) respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, \(\mathrm{d}=4 \sqrt{3} \mathrm{~cm}\) and \(\theta_1=\theta_2=\cos ^{-1}\left(\frac{\mathrm{n}_2}{2 \mathrm{n}_1}\right)\), where refractive index of the block \(\mathrm{n}_2\gt\) refractive index of the outside medium \(\mathrm{n}_1\), then the thickness of the block is ________ cm.

The circuit shown below contains two ideal diodes, each with a forward resistance of \(50\,\Omega \). If the battery voltage is \(6\,V\), the current through the \(100\,\Omega \) resistance (in Amperes) is

A moving coil galvanometer has \(100\) turns and each turn has an area of \(2.0 \mathrm{~cm}^2\). The magnetic field produced by the magnet is \(0.01 \mathrm{~T}\) and the deflection in the coil is \(0.05\) radian when a current of \(10 \mathrm{~mA}\) is passed through it. The torsional constant of the suspension wire is \(\mathrm{x} \times 10^{-5} \mathrm{~N}-\mathrm{m} / \mathrm{rad}\). The value of \(\mathrm{x}\) is _______.

A coil having \(100\) turns, area of \(5 \times 10^{-3} \mathrm{~m}^2\), carrying current of \(1 \mathrm{~mA}\) is placed in uniform magnetic field of \(0.20 \mathrm{~T}\) such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through \(90^{\circ}\) is _______ \(\mu \mathrm{J}\).

The maximum velocity of the photoelectrons emitted from the surface is \(v\) when light of frequency \(n\) falls on a metal surface. If the incident frequency is increased to \(3n\) , the maximum velocity of the ejected photoelectrons will be 

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