Two charges, each equal to \(q\), are kept at \(x = -a\) and \(x = a\) on the \(x-\)axis. A particle of mass \(m\) and charge \(q_0=\frac{q}{2}\) is placed at the origin. If charge \(q_0\) is given a small displacement \((y < < a)\) along the \(y-\)axis, the net force acting on the particle is proportional to

A very long wire \(ABDMNDC\) is shown in figure carrying current \(I. AB\) and \(BC\) parts are straight, long and at right angle. At \(D\) wire forms a circular turn \(DMND\) of radius \(R. AB.\) \(\mathrm{BC}\) parts are tangential to circular turn at \(\mathrm{N}\) and \(D\). Magnetic field at the centre of circle is

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness \(\left(t_{1}\right.\) and \(\left.t_{2}\right)\) as shown in figure. The two different dielectric material are separated by a conducting foil \(F\). The voltage of the conducting foil is \(.....V\)

In parallax method for the determination of focal length of a concave mirror, the object should always be placed :

A spherical body of mass \(2\,kg\) starting from rest acquires a kinetic energy of \(10000\,J\) at the end of \(5^{\text {th }}\) second. The force acted on the body is \(.....N\)

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \(15^{\circ}\) from its original direction. The refractive index of the medium is.

When two resistance \(R_1\) and \(R_2\) connected in series and introduced into the left gap of a meter bridge and a resistance of \(10 \Omega\) is introduced into the right gap, a null point is found at \(60 cm\) from left side. When \(R_1\) and \(R_2\) are connected in parallel and introduced into the left gap, a resistance of \(3 \Omega\) is introduced into the right-gap to get null point at 40 cm from left end. The product of \(R_1 R_2\) is \(.............\Omega\)

For a series \(LCR\) circuit, \(I\) vs \(\omega\) curve is shown \((A)\) To the left of \(\omega_{r}\), the circuit is mainly capacitive. \((B)\) To the left of \(\omega_{r}\), the circuit is mainly inductive. \((C)\) At \(\omega_{r}\), impedance of the circuit is equal to the resistance of the circuit. \((D)\) At \(\omega_{t}\), impedance of the circuit is \(0\). Choose the most appropriate answer from the options given below

A particle of mass \(0.50 \mathrm{~kg}\) executes simple harmonic motion under force \(\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}\). The time period of oscillation is \(\frac{x}{35} s\). The value of \(x\) is _______. (Given \(\pi=\frac{22}{7}\) )

The temperature of a body in air falls from \(40^{\circ} \mathrm{C}\) to \(24^{\circ} \mathrm{C}\) in 4 minutes. The temperature of the air is \(16^{\circ} \mathrm{C}\). The temperature of the body in the next 4 minutes will be:

The angular frequency of alternating current in a \(L-C-R\) circuit is \(100\, rad / s\). The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as \(R\).)