A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity $$\omega$$ with resect to normal axis then the magnetic moment of the loop is :

A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $$\times$$ 10-2 m. The magnetic field at the center of the triangle will be :

A Helmholtz coil has a pair of loops, each with $$N$$ turns and radius $$R$$. They are placed coaxially at distance $$R$$ and the same current $$\mathrm{I}$$ flows through the loops in the same direction. $$P,$$ midway between the centers $$A$$ and $$C$$, is given by [Refer to figure given below] :

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, r$${}_{\alpha }$$ respectively in a uniform magnetic field B. The relation between re, rp, r$${}_{\alpha }$$ is:

Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is :

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of $$30^o$$. The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s2)

A given object takes n times more time to slide down a $$45^{\circ }$$ rough inclined plane as it takes to slide down a perfectly smooth $$45^{\circ }$$ incline. The coefficient of kinetic friction between the object and the incline is :

A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity $$\omega ,$$ the maxium e.m.f. induced in the coil will be:

At the center of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $$\omega$$ about an axis along their common diameter. Calculate the emf induced in their smaller coil after a time t of its start of rotation.

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $$\theta$$ with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the igure. The terminal speed of the copper rod is :

A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle $$\alpha$$ with the horizontal, will be proportional to : (see figure)

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is :

A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :

A force of $$40$$ $$N$$ acts on a point $$B$$ at the end of an $$L$$-shaped object, as shown in the figure. The angle $$\theta$$ that will produce maximum moment of the force about point $$A$$ is given by :

A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod horizontal, a mass $$m$$ is suspended from its end $$A.$$A$$setof$$(m,x)$$ values is recorded. The appropriate variables that give a straight line, when plotted, are :

A thin uniform bar of length $$L$$ and mass $$8$$ m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2$$\upsilon$$ and $$\upsilon$$ respectively. The masses stick to the bar after collision at a distance {L \over 3} and {L \over 6} respectively from the center of the bar. If the br starts rotating about its center of mass as a result of collision, the angular speed of the bar will be :

Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl = 35.5 u)

The major product of the following reaction is :

When 2-butyne is treate with H2/Lindlar's catalyst, compound X is produced as the major product and when treated with Na/liq. NH3 it produces Y as the major product Which of the following statements is correct ?