Engineering Mechanics

Q. A small ring B carries a vertical load P and is supported by two strings BA and BC, the latter of which carries at its free end a weight W = 60 N, as shown in figure. The angles that the strings make with the vertical are shown in the figure, What will be the magnitude of load P if the system remains in equilibrium condition?

1. 80.67 N
2. 115.91 N
3. 58.69 N
4. 131.27 N

Q. A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is

Q. A two member truss ABC is shown in the figure The force (in kN) transmitted in member AB is

Q. 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 mm^2; Young's modulus E = 200 GPa. The force in the truss AB (in N) is

Q.

In the figure, the load P = 1 N, length L = 1m Young's modulus E = 50 GPa, and the cross section of the links is a square with dimension 10 mm X 10 mm. All joints are pin joints.

The stress (in Pa) in the AB is
(Indicate compressive stress by a negative so, and tensile stress by a positive sign)

Q. If a number of forces act on a rigid body, each force may be replaced by an equal parallel force acting through a fixed point, together with a couple. For the rigid body to be in equilibrium.

1. Both resultant force and couple must be zero
2. The resultant couple on the body must be zero
3. The resultant force at the fixed point must be zero
4. None of the above need be zero

Q. Two forces A and B are acting at an angle $\theta$. Their resultant 'R' will make an angle $\alpha$ with the force B, such that sin $\alpha$ is equal to

1. $\frac{A+Bsin\theta }{\sqrt{A^2+B^2-2ABcos\theta }}$
2. $\frac{Bsin\theta }{\sqrt{A^2+B^2+2ABcos\theta }}$
3. $\frac{Asin\theta }{\sqrt{A^2+B^2+2ABcos\theta }}$
4. $\frac{Bcos\theta }{\sqrt{A^2+B^2-2ABcos\theta }}$

Q. If a system is in equilibrium and the position of the system depends upon many independent variables, the principle of virtual work states that the partial derivatives of its total potential energy with respect to each of the independent variable must be

1. -1.0
2. 0
3. 1.0
4. $\infty$

Q. A reel of mass m and radius of gyration k is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel maas m. Symbol g represents the acceleration due to gravity.

The linear acceleration of the reel is

1. $\frac{g{r}^2}{r^2+k^2}$
2. $\frac{g{k}^2}{r^2+k^2}$
3. $\frac{grk}{r^2+k^2}$
4. $\frac{mg{r}^2}{r^2+k^2}$

Q. A lift originally moving downwards at 10 m/s is brought to rest with a constant retardation in a distance of 25 m. The force with which the feet of a passenger of mass 80 kg (take g = 9.8 m/s${}^2$) press downwards on the floor of the lift is

1. 160 N
2. 784 N
3. 944 N
4. 1000 N