Four identical metal butterflies are hanging from a light string of length 5l at equally placed points as shown. The ends of the string are attached to horizontal fixed support. The middle section of the string is horizontal . The relation between the angle `theta_1` and `theta_2` is given by

A partical of mass m is attached to a massless string of length l and is oscillating in a vrtical plane with the other end of the string fixed to a rigid support. The tension in the string at a certain instant is T=kmg .

A heavy particle hanging from a string of length l is projected horizontally with speed sqrtgl . Find the speed of the particle at the point where the tension in the string equals weight of the particle.

A block of mass M si suspended by two strings angles theta_(1) and theta_(2) with the horizontal. Find the tensions in the strings.

In the figure a mass m is hung by a light spring and a light string as shown .Both the spring and the string make an angle theta with the horizontal at equilbrium .If the string is suddenly cut then the instantaneous acceleration of the mass m is :

If a simple pendulum of mass m is released from a horizontal position, find the tension in the string as a function of the angle theta with the horizontal.

A particle is suspended by a light vertical inelastic string of length 1 from a fixed support. At its equilbrium position it is projected horizontally with a speed sqrt(6 g l) . Find the ratio of the tension in the string in its horizontal position to that in the string when the particle is vertically above the point of support.

A particle is suspended by a light vertical inelastic string of length 1 from a fixed support. At its equilbrium position it is projected horizontally with a speed sqrt(6 g l) . Find the ratio of the tension in the string in its horizontal position to that in the string when the particle is vertically above the point of support.

A rod is supported horizontally by means of two strings of equal length as shown in figure. If one of the string is cut. Then tension in other string at the same instant will.

A rod is supported horizontally by means of two strings of equal length as shown in figure. If one of the string is cut. Then tension in other string at the same instant will.

A heavy particle hanging from a fixed point by a light inextensible string of length l is projected horizontally with speed (gl) . Then the speed of the particle and the inclination of the string to the vertical at the instant of the motion when the tension in the string equal the weight of the particle-