Two uiform identical rods AB and CD each of mass M and length L are joined to form a cross as a shown in fig.find the moment of inertia of the cross about a bisector as shown dotted in the figure.
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Three thin metal rods,each of mas M and length dL,are welded to form an equilateral triangle.The moment of inertia of the composite structure about an axis passing through the centre of mas of the structure and perpendicualr to its plane is :

Two spheres each of mass M and radius R//2 are connected with a massless rod of lenth 2R as shown in fig.What will be the oment of inertia of the system about an axis passing through the centre of one of the spheres and prependicular to the rod?

Two magnets each of magnetic moment M are placed so as to form a cross at right angles to each other. The magnetic moment of the system is

Three rods of same material and having the same cross-section are joined as shown in the figure.The tremperature of junction of three rods is : .

Two identical ball bearing in contact with each other and resting on a frictionless table are hit head on by another ball bearing of the same mass moving initially with a speed V shown in the figure. If the collision is elastic, which of the folloiwng shown in the figure is a possible result after collision ?

Two particles , each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2 R . The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod

Two identical thin bar magnets, each of length L and pole strength m are placed at right angles to each other, with the N pole of one touching the S-pole of the other. Find the magnetic moment of the system.

Two metallic rods each of length L, area of cross A_1 and A_2 , having resistance rho_1 and rho_2 are connected in parallel across a d.c. battery. Obtain the expression for the effective resistivity of this combination.

Two identical circular wires P and Q each of radius R and carrying current 'I' are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.

A conducting rod PQ of length 20 cm and resistance 0.1 Omega rests on two smooth parallel rqails of negligible resistance AA' and CC'. It can slide on the rails and the arrangement is positioned betwaeen the poles of a permanent magnet producing unifrom magnetic field B=0.4 T. The rails, the rod and the magneitc field are in the three mutually perpendicular directions as shown in the figure. if hte ends A and C of the rails are short cicuited, find the External force required to move the rod with uniform velocity v=10cm/s.