If a rigid body is subjected to two forces ${\overrightarrow{F}}_1=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}$ acting at $(3,3,4)$ and ${\overrightarrow{F}}_2=-2\hat{\mathrm{i}}-3\hat{\mathrm{j}}-4\hat{\mathrm{k}}$ acting at$(1, 0, 0)$then which of the following is (are) true? 

A uniform rod of mass $m$ and length $L$ is suspended with two massless strings as shown in the figure. If the rod is at rest in a horizontal position the ratio of tension in the two strings $T_1/T_2$ is

Two persons of equal height are carrying a long uniform wooden beam of length $l$. They are at distance $\frac{l}{4}$ and $\frac{l}{6}$ from the nearest ends of the rod. The ratio of normal reactions at their heads is

$\left(1\right) 2:3$

$\left(2\right) 1:3$

$\left(3\right) 4:3$

$\left(4\right) 1:2$

A $T$ shaped object with dimensions shown in the figure is lying on a smooth floor. A force $\overrightarrow{F}$ is applied at the point $P$ parallel to $AB$, such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$

The uniform rod of mass $20 \mathrm{kg}$ and length of $1.6 \mathrm{m}$ is pivoted at its end and swings freely in the vertical plane. Angular acceleration of rod just after the rod is released from rest in the horizontal position.

A uniform rod hinged at its one end is allowed to rotate in the vertical plane. Rod is given an angular velocity $\omega$ in its vertical position as shown in the figure. The value of $\omega$ for which the force exerted by the hinge on the rod is zero in this position is

A uniform rod of length $l$ and mass $m$ is free to rotate in a vertical plane about $A$. The rod initially in a horizontal position is released. The initial angular acceleration of the rod is (Moment of inertia of the rod about $A$ is $\frac{M{l}^2}{3}$)