A body of mass \(500\,g\) moves along \(x\)-axis such that it's velocity varies with displacement \(x\) according to the relation \(v =10 \sqrt{ x } m / s\) the force acting on the body is \(...........\,N\)

Shown in the figure is a shell made of a conductor. It has inner radius \(a\) and outer radius \(b\), and carries charge \(Q\). At its centre is a dipole  \(\vec P\) as shown. In this case

Two point charges \(8 \, \mu C\) and \(-2 \, \mu C\) are located at \(x = 2\) cm and \(x = 4\) cm, respectively on the \(x\)-axis. The ratio of electric flux due to these charges through two spheres of radii \(3\) cm and \(5\) cm with their centers at the origin is _______.

A solution containing active cobalt \({}_{27}^{60}Co\) having activity of \(0.8\,\mu Ci\) and decay constant \(\lambda \) is injected in an animal's body. If \(1 \,cm^3\) of blood is drawn from the animal's body after \(10\, hrs\) of injection, the activity found was \(300\, decays\) per minute. What is the volume of blood that is flowing in the body?..........\(litres\) ( \(ICi = 3.7 \times 10^{10}\) decay per second and at \(t = 10\, hrs\) \({e^{ - \lambda t}} = 0.84\) )

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \(\mathrm{Li}^{++}\)ion in its ground state is given by \(\frac{1}{X} a_0\), where \(X=\) _______. (Where \(\mathrm{a}_0\) is the first Bohr's radius.)

Hot water cools from \(60\,^oC\) to \(50\,^oC\) in the first \(10\,minutes\) and to \(42\,^oC\) in the next \(10\,minutes.\) The temperature of the surroundings is ...... \(^oC\)

The output of the circuit is low (zero) for:

(A) \(\mathrm{X}=0, \mathrm{Y}=0\)
(B) \(X=0, Y=1\)
(C) \(X=1, Y=0\)
(D) \(\mathrm{X}=1, \mathrm{Y}=1\)
Choose the correct answer from the options given below :

A metal wire of uniform mass density having length \(L\) and mass \(M\) is bent to form a semicircular arc and a particle of mass \(m\) is placed at the centre of the arc. The gravitational force on the particle by the wire is _______.

An electron gun is placed inside a long solenoid of radius \(\mathrm{R}\) on its axis. The solenoid has \(\mathrm{n}\) turns/length and carries a current \(I\). The electron gun shoots an electron along the radius of the solenoid with speed \(v\). If the electron does not hit the surface of the solenoid, maximum possible value of \({v}\) is (all symbols have their standard meaning)

An \(L-\) shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \(AB = BC\), and the angle made by \(AB\) with downward vertical is \(\theta\) then

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is ___________ .
\(\left(\tan ^{-1}(1.52)=57.7^{\circ}\right.\), refractive indices of air and glass are 1.00 and 1.52 , respectively)