A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then :

A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common centre O is :

A beam of protons with speed 4 × 105 ms–1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to : (Mass of the proton = 1.67 $$\times$$ 10–27 kg, charge of the proton = 1.69 $$\times$$ 10–19 C)

The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 $$\times$$ 105 ms–1 making an angle 60o with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to (mass of proton = 1.67 $$\times$$ 10–27 kg, charge of the proton = 1.6 $$\times$$ 10–19 C)

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45o with the vertical. Then F equal : (Take g = 10 ms–2 and the rope to be massless)

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv2 where v is its speed. The maximum height attained by the ball is :

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate {{dM\left( t \right)} \over {dt}} = bv2(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is : (g = 10 ms–2)

A particle moving in the xy plane experiences a velocity dependent force $$\overrightarrow{F}=k\left(v_y\hat{i}+v_x\hat{j}\right)$$ , where vx and vy are the x and y components of its velocity $$\overrightarrow{v}$$ . If $$\overrightarrow{a}$$ is the acceleration of the particle, then which of the following statements is true for the particle?

An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length $$l$$ and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is :

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate {{dB} \over {dt}} = 0.032 Ts–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 $$\times$$ 10–8 $$\Omega$$m)

An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency $$\omega$$, the average power loss in the loop due to Joule heating is :

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil? Three positions shown describe : (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit.

A shown in the figure, a battery of emf $$\epsilon$$ is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = tc (tc is the time constant of the circuit) is :

At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loop is :

A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

A long solenoid of radius R carries a time (t) - dependent current I(t)=I0t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 $$\le$$ t $$\le$$ 1, the induced current (IR) and the induced EMF(VR) in the ring change as :

Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $$\varphi$$i. The magnetic flux through the area of the circular coil area is given by $$\varphi$$0. Which of the following option is correct?

A uniform rod of length ‘$$l$$’ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $$\omega$$ the rod makes an angle $$\theta$$ with it (see figure). To find $$\theta$$ equate the rate of change of angular momentum (direction going into the paper) {{m{l^2}} \over {12}}{\omega ^2}\sin \theta \cos \theta about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH and FV about the CM. The value of $$\theta$$ is then such that :

Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ‘m’ and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is :