A heavy string of mass m hangs between two fixed points A and B at the same level. The tangents to the string at A and B are at an angle $\theta$ with the horizontal as shown in the figure. The tension in the string at the lowest point is

Q. A flexible chain of mass $m$ hangs between two fixed points $A$ and $B$ at the same level. The inclination of the chain with the horizontal at the two points of support is $\theta$. The tension at the midpoint $C$ of the chain is

Q. A flexible chain of mass $M$ hangs between two fixed points A and B at the same level. The inclination of the chain with the horizontal at the two points of support is $\theta$. The tension at the mid-point of the chain is

Q. A ball is projected with horizontal velocity $v_o=\sqrt{9gR}$ at the bottom most point attached with inextensible string of length R and fixed at O as shown. Tension in the string in horizontal position

Q. A uniform cylinder of mass $M$ lies in a fixed plane inclined at angle $\theta$ with horizontal. A light string is tied to the cylinder at the right most point, and a mass $m$ hangs from the string, as shown in. Assume that the coefficient of friction between the cylinder and the inclined plane is sufficiently large to prevent slipping. For the cylinder to remain static, the value of m is

Q. A small body of mass $m=10\text{kg}$ hangs at one end of a string of length $l$, the other end of which is fixed. It is given horizontal velocity $u$ at its lowest position. The string just becomes slack, when it covers an angle ${120}^{\circ }$ with the initial position. Find the tension in the string at the point of projection. Take $g=10{\text{m/s}}^2$