Physics

An electron and a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field B = B₀i, each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

A rectangular conducting loop consists of two wires on two opposite sides of length l joined together by rods of length d. The wires each are of the same material but with cross-sections differing by a factor of 2. The thicker wire has a resistance R and the rods are of low resistance, which in turn are connected to a constant voltage source V0. The loop is placed in a uniform magnetic field B at 45° to its plane. Find T, the torque exerted by the magnetic field on the loop about an axis through the centres of rods.

A 100 turn rectangular coil ABCD (in X-Y plane) is hung from one arm of a balance (shown in figure). A mass 500 g is added to the other arm to balance the weight of the coil. A current 4.9 A passes through the coil and a constant magnetic field of 0.2 T acting inward (in x-z plane) is switched on such that only arm CD of length 1 cm lies in the field. How much additional mass m must be added to regain the balance?

A 100 turn rectangular coil ABCD (in X-Y plane) is hung from one arm of a balance (shown in figure). A mass 500 g is added to the other arm to balance the weight of the coil. A current 4.9 A passes through the coil and a constant magnetic field of 0.2 T acting inward (in x-z plane) is switched on such that only arm CD of length 1 cm lies in the field. How much additional mass m must be added to regain the balance?

For two vectors A and B, A B A B + = − is always true when (a) A B = ≠ 0 (b) A⊥ B (c) A B = ≠ 0 and A and B are parallel or anti parallel (d) when either A or B is zero.

For a particle performing uniform circular motion, choose the correct statement(s) from the following:

(a) Magnitude of particle velocity (speed) remains constant.

(b) Particle velocity remains directed perpendicular to radius vector.

(c) Direction of acceleration keeps changing as particle moves.

(d) Angular momentum is constant in magnitude but direction keeps changing.

A capacitor is made of two circular plates of radius R each, separated by a , distance d << R. The capacitor is connected to a constant voltage. A thin conducting disc of radius r << R and thickness t << r is placed at the centre of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is m.

Following are four different relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one (s) : 

(a) V_av= $\frac{1}{2}[\mathit{v}\left({\mathit{t}}_1\right)+\mathit{v}({\mathit{t}}_2\left)\right]$

(b) V_av=   $\frac{\mathit{r}{(\mathit{t}}_2)-\mathit{r}{(\mathit{t}}_1)}{{\mathit{t}}_2-{\mathit{t}}_1}$

(c) V_av= $\frac{1}{2}\left[\mathit{v}\left({\mathit{t}}_1\right)-\mathit{v}\left({\mathit{t}}_2\right)\left({\mathit{t}}_2-{\mathit{t}}_1\right)\right]\mathit{}\mathit{}$

$\left(\mathit{d}\right)\mathbf{V}\mathbf{a}\mathbf{v}=\mathbf{}\frac{\mathit{v}{(\mathit{t}}_2)-\mathit{v}{(\mathit{t}}_1)}{{\mathit{t}}_2-{\mathit{t}}_1}\mathbf{}$

A particle slides down a frictionless parabolic (y + x² ) track (A – B – C) starting from rest at point A (Fig. 4.2). Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then

(a) KE at P = KE at B

(b) Height at P = height at A

(c) Total energy at P = total energy at A

(d) Time of travel from A to B = time of travel from B to P.

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as ε= αU where α = 2V^-1. A similar capacitor with no dielectric is charged to U₀= 78 V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.