A girl was wearing a set of earings made of the line segments, semicircular arcs and arcs of quadrant of cricles as shown in the figure. Calculate total length of the metal wire required to make a set of ear rings

A uniform semicircular ring of mass m and radius r is hinged at end A so that it can rotate freely about end A in the vertical plane as shown in the figure. Calculate angle made by line AB with vertical in equilibrium position and time period of small oscillation of ring.

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 12.12. Find : (i) the total length of the silver wire required. (ii) the area of each sector of the brooch.

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 15.16. Find: (i) the total length of the silver wire required (ii) the area of each sector of the brooch.

In the circle shown in the figure, the length of the arc ACB is 3 times the length of the arc AB. What is the length of the line segment AB ?

A wire of length L= 20 cm is bent into a semicircular arc and the two equal halves of the arc are uniformly charged with charges +Q and -Q as shown in the figure. The magnitude of the charge on each half is |Q| =10^(3) epsilon_(0) , where epsilon_(0) is the permittivity of free the space. The net electric field at the center O is

A ring of radius R is made of a thin wire of material of density rho having cross section area a. The ring rotates with angular velocity omega about an axis passing through its centre and perpendicular to the plane. If we consider a small element of the ring,it rotates in a circle. The required centripetal force is provided by the component of tensions on the element towards the centre. A small element of length dl of angular width d theta is shown in the figure. If for a given mass of the ring and angular velocity, the radius R of the ring is increased to 2R , the new tension will be

In the figure above, point O is the center of the circle, line segments LM and MN are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. If the circumference of the circle is 96, what is the length of minor arc overset(frown)(LN) ?

A ring of radius R is made of a thin wire of material of density rho having cross section area a. The ring rotates with angular velocity omega about an axis passing through its centre and perpendicular to the plane. If we consider a small element of the ring,it rotates in a circle. The required centripetal force is provided by the component of tensions on the element towards the centre. A small element of length dl of angular width d theta is shown in the figure. If T is the tension in the ring, then

A potentiometer circuit is shown in Figure 3. AB is a uniform metallic wire having length of 2 m and resistance of 8Omega . The batteries E_(1) and E_(2) have emfs of 4V and 1.5 V and their internal resistance are 1Omega" and "2Omega respectively. If the jockey J is made to touch the wire AB at a point C such that the galvanometer (G) shows no defection. Calculate the length AC.

A potentiometer circuit is shown in Figure 3 below. AB is a uniform metallic wire having length of 2m and resistance of 8Omega . The batteries E_(1) and E_(2) have emfs of 4V and 1.5V and their internal resistances are 1Omega and 2Omega respectively. Now the jockey J is made to touch the wire AB at a point C such that the galvanometer (G) shows no deflection. Calculate the length AC.