A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:

A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is : (Assume that the current is flowing in the clockwise direction.)

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = $$-$$ $$\alpha$$x2. The distance at which the particle stops :

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $$\theta$$ as shown in figure. The coefficient of kinetic friction is $$\mu$$k. then, the block's acceleration 'a' is given by : (g is acceleration due to gravity)

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s2. The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20 kg each, is ____________ N. [Take g = 10 m/s2 and $$\mu$$s = 0.2]

A force $$\overrightarrow{F}=(40\hat{i}+10\hat{j})N$$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\overrightarrow{r}$$ at time t = 10 s, will be :

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = {F_0}\left[ {1 - {{\left( {{{t - T} \over T}} \right)}^2}} \right] Where F0 and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms-2. The gases come out at a relative speed of 500 ms$$-$$1 with respect to the rocket : [Use g = 10 m/s2]

The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s2)

Statement : 1 If three forces $${\overrightarrow{F}}_1,{\overrightarrow{F}}_2$$ and $${\overrightarrow{F}}_3$$ are represented by three sides of a triangle and $${\overrightarrow{F}}_1+{\overrightarrow{F}}_2=-{\overrightarrow{F}}_3$$, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement : 2 A triangle made up of three forces $${\overrightarrow{F}}_1$$, $${\overrightarrow{F}}_2$$ and $${\overrightarrow{F}}_3$$ as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below :

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given m = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile. The correct applied force vs distance graph will be :

Figure shows a circuit that contains four identical resistors with resistance R = 2.0$$\Omega$$, two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9V. The current 'i' just after the switch 'S' is closed will be :

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 $$\times$$ 10$$-$$4 Wb/m2 and the angle of dip is 60$${}^{\circ }$$. The emf induced between the tips of the plane wings will be __________.

A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure Two resistors R1 and R2 are connected across the ends of the rails. There is a uniform magnetic field $$\overrightarrow{B}$$ pointing into the page. An external agent pulls the bar to the left at a constant speed v. The correct statement about the directions of induced currents I1 and I2 flowing through R1 and R2 respectively is :

The magnetic field in a region is given by \overrightarrow B = {B_o}\left( {{x \over a}} \right)\widehat k. A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity $$\overrightarrow{v}$$ = v0$$\hat{i}$$. The emf induced in the loop is :

The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance.