Engineering Mechanics (EM)

Q:   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

• A:  T1=100 N and T2=0 N
• B:  T1=0 N and T2=100 N
• C:  T1=75NandT2=25N
• D:  T1=25NandT2=75N

Q:   A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t=0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s² and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

• A:  1
• B:  2
• C:  4
• D:  infinity

Q:   A partical of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t)=t2,θ(t)=t, where t is time. The kinetic energy of the partical at time t=2 is

• A:  4
• B:  12
• C:  16
• D:  24

Q:   The following figure shows the velocity-time plot for a particle traveling along a staright line. The distance coverd by the particle from t = 0 to t = 5 s is ____________ m,

Q:   Two disks A and B with identical mass (m) and radius (R) are initialy at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is

• A:  √(3/4)
• B:  √(3/2)
• C:  1
• D:  √2

Q:   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 cosθ=0.8 and sinθ=0.6.
Acceleration due to gravity g = 10 m/s2

Q:   A mass of 2000 kg is currently being lowered at a velocity of 2 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is 150kg−m². On applying the brake, the mass is brought to rest in a distance of 0.5 m. The energy absorbed by the brake (in kJ) is __________

Q:   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 __________

Q:   A wheel of radius r rolls without slipping on a horizontal surface shown below. If The velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) 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 mm², Young’s modulus E = 200 GPa. The force in the truss AB (in N) is ______.