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)
A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?
Take the acceleration due to gravity to be π = 9.8 m/s2. Options have been rounded off to one decimal place.
![GATE ME 2023 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 1 English](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1lz4aprcb/bb62242d-4b3b-4c03-8081-a8a4d00da476/3a7557b0-4c2e-11ef-8da2-8d5e9df213cb/file-jaoe38c1lz4aprcc.png?format=png)
A rigid homogeneous uniform block of mass 1 kg, height h = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse IF is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IF required to topple the block is
![GATE ME 2022 Set 2 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 6 English](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m0883y1e/f659a1d4-28d2-4db3-8593-e7415c41fa59/638c6f20-6223-11ef-ad9a-5dfeb0493e4e/file-jaoe38c1m0883y1f.webp?format=webp)
A rigid body in the X-Y plane consists of two point masses (1 kg each) attached to the ends of two massless rods, each of 1 cm length, as shown in the figure. It rotates at 30 RPM counter-clockwise about the Z-axis passing through point O. A point mass of β2 kg, attached to one end of a third massless rod, is used for balancing the body by attaching the free end of the rod to point O. The length of the third rod is ______ cm.
![GATE ME 2022 Set 2 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 5 English](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m087s0hf/dfea40f6-5a03-41e3-93ca-28087bf6b74c/17ba4c30-6222-11ef-ad9a-5dfeb0493e4e/file-jaoe38c1m087s0hg.png?format=png)