A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 $$\times$$ 10$$-$$19C)

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the radio of the magnetic field at the central of the loop (BL) to that at the center of the coil (BC), i.e. {{{B_L}} \over {{B_C}}} will be :

An insulating thin rod of length $$l$$ has a linear charge density $$\rho \left(x\right)$$ = {\rho _0}{x \over l} on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is -

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then -

In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 $$\times$$ 10–19 C Mass of the electron = 9.1 $$\times$$ 10–31 kg]

The region between y = 0 and y = d contains a magnetic field $$\overrightarrow{B}=B\hat{z}$$. A particle of mass m and charge q enters the region with a velocity $$\overrightarrow{v}=v\hat{i}.$$ If d $$=$$ {{mv} \over {2qB}}, the acceleration of the charged particle at the point of its emergence at the other side is :

A particle of mass m and charge q is in an electric and magnetic field given by $$\overrightarrow{E}=2\hat{i}+3\hat{j};\overrightarrow{B}=4\hat{j}+6\hat{k}.$$ The charged particle is shifted from he origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the total work done is :

As shown in the figure, two infinitely long, identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10–4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ($$\mu$$0 = 4$$\pi$$ $$\times$$ 10–7 NA–2) :

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constant, k1 and k2 will be :

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30o with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $$\mu$$ = 0.2. The difference between the accelerations of the blocks, in case (B) and case (A) will be : (g = 10 ms–2)

Two blocks A and B of masses mA = 1 kg and mB = 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : [Take g = 10 m/s2]

A bullet of mass 20 g has an initial speed of 1 ms–1 , just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of 2.5 × 10–2 N, the speed of the bullet after emerging from the other side of the wall is close to :

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is : [Take g = 10 m/s2]

A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to m$$\gamma$$u2 (where m is mass of the ball, u is its instantaneous velocity and $$\gamma$$ is a constant). Time taken by the ball to rise to its zenith is :

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms$$-$$2)

Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle $$\theta$$ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle $$\theta$$ is -

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45o at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms$$-$$2

The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of 1 cm s-1. At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of the loop. If the resistance of L is 1.7 $$\Omega$$, the current in the loop at that instant will be close to :

A very long solenoid of radius R is carrying current I(t) = kte–at(k > 0), as a function of time (t $$\ge$$ 0). counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by :-

Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of 10–3 Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is :-