A ram in the form of a rectangular body of size $l = 9 \text{ m}$ and $b = 2 \text{ m}$ is suspended by two parallel ropes of lengths $7 \text{ m}$. Assume the center-of-mass of the body is at its geometric center and $g = 9.81 \text{ m/s}^2$. For striking the object P with a horizontal velocity of $5 \text{ m/s}$, what is the angle $\theta$ with the vertical from which the ram should be released from rest?
![GATE ME 2024 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 17 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx6r8vnx/c6e2d554-95c7-458f-8617-31882ab74a98/02c776e0-25f0-11ef-b9f4-0b0f0dea04e0/file-6y3zli1lx6r8vny.png?format=png)
A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along x-axis and another at point B along y-axis. For the body to be in equilibrium, the third point load acting at point O must be
![GATE ME 2024 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 16 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx6rd87d/d89238f7-f720-4d4a-96fb-8fd1cee97274/7bb3bb90-25f0-11ef-b9f4-0b0f0dea04e0/file-6y3zli1lx6rd87e.png?format=png)
A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of $P = 100$ kN and $Q = 50$ kN. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is _________ kN (rounded off to 1 decimal place).
![GATE ME 2024 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 15 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx72ywot/5741a425-839d-479a-8d97-3e4186c4ccf1/db074ad0-261d-11ef-a279-4f9760cfcb83/file-6y3zli1lx72ywou.png?format=png)
The velocity field of a two-dimensional, incompressible flow is given by $\overrightarrow{V} = \ 2sin{h}\,x\,\hat{i} + v(x,y)\hat{j}$ where $ \hat{i}$ and $\underset{\dot{}}{j}$ denote the unit vectors in x and y directions, respectively. If $v(x, 0) = cosh\ x$, then $v(0,-1)$ is