# Questions & Answers of Engineering Mechanics

#### Topics of Engineering Mechanics 51 Question(s) | Weightage 03 (Marks)

Question No. 16

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 __________

Question No. 17

A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is

Question No. 40

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/$s^2$

Question No. 41

A two-member truss PQR is supporting a load W. The axial forces in members PQ and QR are respectively

Question No. 116

A point mass having mass M is moving with a velocity V at an angle $\theta$to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is

Question No. 140

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 $150\mathrm{kg}-\mathrm m^2$. 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 __________

Question No. 216

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

Question No. 219

A rigid link PQ is undergoing plane motion as shown in the figure ($\style{font-family:'Times New Roman'}{\left(V_{P\;}and\;V_Q\;are\;non-zero\right)}.$\style{font-family:'Times New Roman'}{V_{QP}}$is the relative velocity of point Q with respect to point P. Which one of the following is TRUE? ##### Show Answer Question No. 240 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 __________ ##### Show Answer Question No. 241 A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed $v$ of the disc when it reaches position B is _________ m/s. Acceleration due to gravity g = 10 m/s2. ##### Show Answer Question No. 242 A rigid rod (AB) of length $L=\sqrt{2}$ m is undergoing translational as well as rotational motion in the x-y plane (see the figure). The point A has the velocity$V_{1\;}=\widehat i+2\widehat j$m/s. The end B is constrained to move only along the x direction. The magnitude of the velocity V2 (in m/s) at the end B is __________ ##### Show Answer Question No. 23 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 ________ ##### Show Answer Question No. 26 Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0m; cross-sectional area is 200 mm2, young’s modulus E = 200GPa. The force in the truss AB (in N) is ______. ##### Show Answer Question No. 49 For the turss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively ##### Show Answer Question No. 50 A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20% . The height (in m) to which the ball will rise is _____. ##### Show Answer Question No. 116 A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be____. ##### Show Answer Question No. 140 The initial velocity of an object is 40 m/s. The acceleration a of the object is given by the following expression: a = – 0.1 v Where v is the instantaneous velocity of the object. The velocity of the object after 3 seconds will be____. ##### Show Answer Question No. 142 For the truss shown in figure , the magnitude of the force (in kN) in the member SR is ##### Show Answer Question No. 228 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 ##### Show Answer Question No. 236 The value of moment of inertia of the section shown in the figure about the axis-XX is ##### Show Answer Question No. 237 Figure shows a wheel rotating about O2. Two points A and B located along the radius of wheel have speeds of 80 m/s and 140 m/s respectively. The distance between the points A and B is 300 mm. The diameter of the wheel (in mm) is__________ ##### Show Answer Question No. 255 A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections A and B on the bullet engage in each of the slots. Helical slots are such that one turn of helix is completed over a distance of 0.5 m. If velocity of bullet when it exits the barrel is 20 m/s, its spinning speed in rad/s is _______. ##### Show Answer Question No. 19 A circular object of radius r rolls without slipping on a horizontal level floor with center having velocity V. The velocity at the point of contact between the object and floor is ##### Show Answer Question No. 41 A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure.Block R is tied to the wall by a massless and inextensible string PQ.If the coefficient of static friction for all surfaces is 0.4, the minimum force F (in n kN) needed to move the block S is ##### Show Answer Question No. 45 A block weighing 200 N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2, respectively. The block is acted upon by a horizontal force (in newton) P=10t, where t denotes the time in seconds. The velocity (in m/s) of the block attained after 10 seconds is _______ ##### Show Answer Question No. 117 A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is _______ ##### Show Answer Question No. 146 A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction between the crate and the truck surface is 0.3. The maximum value of acceleration (in m/s2) of the truck such that the crate does not slide down is _______ ##### Show Answer Question No. 219 A mass m1 of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is ##### Show Answer Question No. 241 A body of mass (M) 10 kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is 0.5. The body slides down the plane and attains a velocity of 20 m/s. The distance travelled (in meter) by the body along the plane is _______ ##### Show Answer Question No. 244 An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is ##### Show Answer Question No. 316 In a statically determinate plane truss, the number of joints (j) and the number of members (m) are related by ##### Show Answer Question No. 320 A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of 4 Hz. The maximum acceleration (m/s2) of the mass is _______ ##### Show Answer Question No. 342 For the truss shown in the figure, the forces F1 and F2 are 9 kN and 3 kN, respectively. The force (in kN) in the member QS is ##### Show Answer Question No. 346 A frame is subjected to a load P as shown in the figure. The frame has a constant flexural rigidity EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is ##### Show Answer Question No. 347 A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the Y-Y axis, stands on a rough level floor as shown in the figure. A force P is applied at mid-height on the wardrobe so as to tip it about point Q without slipping. What are the minimum values of the force (in newton) and the static coefficient of friction μ between the floor and the wardrobe, respectively? ##### Show Answer Question No. 350 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 _______ ##### Show Answer Question No. 33 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 ##### Show Answer Question No. 44 A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in the figure, where the wrapping angle is 180°. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied, in N.m. is ##### Show Answer Question No. 48 Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F as shown in figure. All the joints are hinged. If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is ##### Show Answer Question No. 49 Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F as shown in figure. All the joints are hinged. The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is ##### Show Answer Question No. 22 The coefficient of restitution of a perfectly plastic impact is ##### Show Answer Question No. 32 A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force Fx (in N) exerted by the rubber band as a function of distance x (in m) is given by Fx = 300x2. If the stone is displaced by 0.1m from the un-stretched position (x = 0) of the rubber band, the energy stored in the rubber band is ##### Show Answer Question No. 43 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 ##### Show Answer Question No. 10 A block weighing 981 N is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is µ = 0.2.A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 100 N. What will be the tension, T (in N) in the cable if the man is just able to move the block to the right? ##### Show Answer Question No. 41 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 ##### Show Answer Question No. 9 A straight rod of length L(t), hinged at one end and freely extensible at the other end, rotates through an angle about the hinge. At time t, L(t) =1 m,$\dot L\left(t\right)$= 1 m/s, $\theta \left(t\right)=\frac{\mathrm{\pi }}{4}$ rad and$\dot\theta\left(t\right)\$= 1 rad/s. The magnitude of the velocity at the other end of the rod is

Question No. 10

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

Question No. 33

A circular disk of radius R rolls without slipping at a velocity v. The magnitude of the velocity at point P (see figure) is

Question No. 34

Consider a truss PQR loaded at P with a force F as shown in the figure

The tension in the member QR is

A block of mass M is released from point P on a rough inclined plane with inclination angle $\theta$, shown in the figure below. The coefficient of friction is $\mu$. If $\mu <\mathrm{tan}\theta$, then the time taken by the block to reach another point Q on the inclined plane, where PQ = s, is