Which of the following statement(s) is/are correct?

A wooden block performs $$SHM$$ on a frictionless surface with frequency, $${v_0}.$$ The block carries a charge $$+Q$$ on its surface . If now a uniform electric field $$\overrightarrow E $$ is switched- on as shown, then the $$SHM$$ of the block will be

Which of the field patterns given below is valid for electric field as well as for magnetic field ?

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $${x_1}\left( t \right) = A\sin \omega t$$ and $${x_2}\left( t \right) = A\sin \left( {\omega t + {{2\pi } \over 3}} \right)$$. Adding a third sinusoidal displacement $${x_3}\left( t \right) = B\sin \left( {\omega t + \phi } \right)$$ brings the mass to a complete rest. The values of B and $$\phi $$ are

A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the center of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is

A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of $$60^\circ $$ to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s², is

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2 %, the relative percentage error in the density is

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is

A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence $$\theta$$. The reflected (R) and transmitted (T) intensities, both as function of $$\theta$$, are plotted. The correct sketch is

A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the xy-plane and a steady current I flows through the wire. The z-component of the magnetic field at the centre of the spiral is

Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are fully immersed in a fluid of density d_F. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision,

A series RC-current is connected to AC voltage source. Consider two cases : (A) When C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current I_R through the resistor and voltage V_C across the capacitor are compared in the two cases. Which of the following is/are true?

A series RC combination is connected to an AC voltage of angular frequency $$\omega$$ = 500 rad/s. If the impedance of the RC circuit is R$$\sqrt{1.25}$$, the time constant (in millisecond) of the circuit is __________.

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the spheres is A $$\times$$ 10^Z (where 1 < A < 10). The value of Z is _____________.

Two batteries of different emfs and different internal resistance are connected as shown. The voltage across AB in volts is __________.

Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature R = 6 cm as shown. Consider oil to act a thin lens. An object S is placed 24 cm above water surface. The location of its image is at x cm above the bottom of the tank. Then x is __________.

One mole of a monatomic gas is taken through a cycle ABCDA as shown in the PV diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.

	Column I		Column II
(A)	Process A$$ \to $$ B	(P)	Internal energy decreases.
(B)	Process B$$ \to $$C	(Q)	Internal energy increase.
(C)	Process C$$ \to $$D	(R)	Heat is lost.
(D)	Process D$$ \to $$A	(S)	Heat is gained.
		(T)	Work is done on the gas.

Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $$\lambda$$_f. Match each system with statements given in Column II describing the nature and wavelength of the standing waves :