# Questions & Answers of Free Body Diagrams and Equilibrium

## Weightage of Free Body Diagrams and Equilibrium

Total 14 Questions have been asked from Free Body Diagrams and Equilibrium topic of Engineering Mechanics subject in previous GATE papers. Average marks 1.57.

A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.

The tensions in the strings are

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Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q, where the local radius of curvature is 2 m as shown in the figure. Assuming g = 10  m/s2 , the normal force (in N) at Q is _______ (correct to two decimal places).

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The rod PQ of length $L=\sqrt{2}$ , and uniformly distributed mass of $M=10\;kg$, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ.  Assume acceleration due to gravity, $g=10\;m/s^2$. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the figure is $(ML^2/12)$. At this instant, the magnitude of angular acceleration (in radian/s2) of the rod is____________

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A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force $F$ such that the string makes an angle of $30^\circ$ with the vertical. The magnitude of force $F$ (in N) is __________

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A block of mass $m$ rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is 0.25. The string can withstand a maximum force of 20 N. The maximum value of the mass $(m)$ for which the string will not break and the block will be in static equilibrium is ____________ kg.

Take $\cos\theta=0.8$ and $\sin\theta=0.6$.

Acceleration due to gravity g = 10 m/$s^2$

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A force F is acting on a bent bar which is clamped at one end as shown in the figure.

The CORRECT free body diagram is

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An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is __________

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Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0 m; cross-sectional area is 200 mm2, Young’s modulus E = 200 GPa. The force in the truss AB (in N) is ______.

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A weight of 500 N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respectively

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A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless contact at the floor (B) and the wall (A), the magnitude of the force P (in newton) required to maintain equilibrium of the ladder is _______

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A pin jointed uniform rigid rod of weight W and length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is

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A 1 kg block is resting on a surface with coefficient of friction μ = 0.1. A force of 0.8 N is applied to the block as shown in figure. The friction force is

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A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of 2L/3 from the hinge so that the rod swings to the right. The reaction at the hinge is

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A cantilever type gate hinged at Q is shown in the figure. P and R are the centers of gravity of the cantilever part and the counterweight respectively. The mass of the cantilever part is 75 kg. The mass of the counterweight, for static balance, is