Engineering Mechanics

Q.

State the law of simple pendulum.

Q. The ratio of tension on the tight side to that of the slack ride in a flat belt drive is

1. Proportional to the product of coefficient of friction and lap angle
2. An exponential function of the product of coefficient of friction and lap angle
3. Proportional to lap angle
4. Proportional to the coefficient of friction

Q. A wheel of radius r rolls without slipping on a horizontal surface shwon below. If the velocity of point P is $10\frac{m}{s}$ in the horizontal direction, the magnitude of velocity of point Q $\left(in\frac{m}{s}\right)$ is

Q. The tension in the cable supporting a lift moving upwards is twice the tension when the lift moves downwards. What is the acceleration of the lift?

1. g/4
2. g/3
3. g/2
4. g

Q. The figure shows a pair of pin-jointed gripper - tongs holding an object weighing 2000 N. The coefficient of friction $\left(\mu \right)$ at the gripping surface is 0.1. XX is the line of action of the input force and YY is the line of application of gripping force. If the pin-joint is assumed to be frictionless, the magnitude of force F required to hold the weight is

1. 1000 N
2. 2000 N
3. 2500 N
4. 5000 N

Q. For the truss loaded as shown in figure, force in the member AC is

1. $\sqrt{2}$ kN compression
2. $\frac{\sqrt{3}}{2}$ kN compression
3. $\frac{\sqrt{3}}{2}$ kN tension
4. $\sqrt{2}$ kN tension

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 car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 seconds interval. The acceleration of the car is

1. $7m/s^2$
2. $50m/s^2$
3. $25m/s^2$
4. $10m/s^2$

Q. A rod of length 1 m is sliding in a corner as shown in figure. At an instant when the rod makes an angle of 60 degrees with the horizontal plane, the velocity of point A on the rod is $1\frac{m}{s}$. The angular velocity of the rod at the instant is

1. $2\frac{rad}{s}$
2. $1.5\frac{rad}{s}$
3. $0.5\frac{rad}{s}$
4. $0.75\frac{rad}{s}$

Q. Two forces are acting on a point at an angle of $\alpha$ and $\beta$ as shown in figure. If the sum of these forces is 700 N directed vertically, What are the angles $\alpha$ and $\beta$?

1. $\alpha ={55.95}^{\circ },\beta ={45.58}^{\circ }$
2. $\alpha ={45.58}^{\circ },\beta ={55.95}^{\circ }$
3. $\alpha ={90}^{\circ },\beta ={30}^{\circ }$
4. $\alpha ={40.166}^{\circ },\beta ={53.73}^{\circ }$

Q. In a statically determinate plane truss, the number of joints (j) and the number of members (m) are related by

1. $j=2m-3$

2. $m=2j+1$

3. $m=2j-3$

4. $m=2j-1$

Q.

A force is resolved into components$P$ and $Q$ equally inclined to it. Then,

1. $P=2Q$

2. $2P=Q$

3. $P=Q$

4. NONE

Q. A simple pendulum of length of 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of $5\frac{m}{s}.$ The net force on bob at the mean position is

1. Zero

2. 2.5 N

3. 5 N

4. 25 N

Q. A uniform rod of length 'l' is kept vertically on a horizontal smooth surface at a point O. If it is rotated slightly and released, it falls down on the horizontal surface. the lower end will remain

1. at O
2. at a distance less than l/2 from O
3. at a distance l/2 from O
4. at a distance larger than l/2 from O

Q. A weight 'W' is supported by two cables as shown in the figure below. The tension in the cable making an angle $\theta$ will be the minimum when the value of $\theta$ is

1. $0^o$
2. ${30}^o$
3. ${45}^o$
4. ${60}^o$

Q. $\text{Two rectangular blocks of weight}{W}_1\text{and}{W}_2\text{are connected by a flexiable string and rest upon a horizontal and an inclined plane respectively with the cord passing over a pulley as shown , n figure. If}{W}_1=W_2\text{and coefficient of static frictionn is}\mu \text{for all contiguous surface. What should be the inclination of the inclined plane at which motion of system will impend?}$

1. $\tan \frac{\alpha }{2}=\mu$

2. $\sin \alpha =\sqrt{1-{\mu }^2}$

3. $\tan \alpha =\mu$

4. $\tan \alpha =(1-\mu )$

Q. A truss consists of horizontal members (AC, CD, DB, and EF) and vertical members (CE and DF) having length l each. The members AE, DE and BF are inclined at ${45}^{\circ }$ to the horizontal. For the uniformly distributed load p per unit length on the members EF of the truss shown in figure given below, the force in the member CD is

1. $\frac{pl}{2}$
2. $pl$
3. 0
4. $\frac{2pl}{3}$

Q. The greatest possible acceleration or deceleration that a train may have is $a$ , and its maximum speed is $v$ and total distance is $s$. What is the minimum time in which the train can get from one station to another?

1. $t=\frac{s}{v}+\frac{v}{a}$

2. $t=\frac{s}{v}$

3. $t=\frac{s}{v}-\frac{v}{a}$

4. $t=\frac{s}{v}+2\frac{v}{a}$
   

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

1. $\sqrt{3}V$
2. $\sqrt{3}\frac{V}{2}$
3. $\frac{V}{2}$
4. $\frac{2V}{\sqrt{3}}$

Q. A sphere is fired downward into a medium with an initial speed of 27 m/s. If it experiences a deceleration $\ddot{x}=(-6t)m/s^2$, where t is in seconds. Determine the distance travelled before it stops.(in m)

1. 45
2. 54
3. 27
4. 81

Q. A ball is thrown vertically into the air at $36m/s$. After 3 sec., another ball is thrown vertically, the initial velocity the second ball have to pass the first ball must at $30$ meter from the ground in (m/s) is___

1. 25

Q.

Two steel truss members, AC and BC, each having cross sectional area of $100m{m}^2,$ 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

1. 8.17
2. 11.15
3. 14.14
4. 22.30

Q. A uniform rod of mass 300 g and length 50 cm rotates at a uniform angular speed of 2 rad/s about an axis perpendicular to the rod through an end. The angular momentum of the rod about the axis of rotation, the speed of the centre of the rod and its kinetic energy respectively are_______, _______ and _______.

1. $0.05kg-m^2/s,0.5cm/s,0.05J$
2. $0.5kg-m^2/s,0.5m/s,0.5J$
3. $0.05kg-m^2/s,50cm/s,0.05J$
4. $0.05kg-m^2/s,50m/s,5J$

Q. A wire rope is designated as $6\times 19$ standard hoisting. The numbers $6\times 19$ represent

1. diameter in millimeter $\times$ length in meter
2. diameter in centimeter $\times$ length in meter
3. number of strands $\times$ number of wires in each strand
4. numbers of wires in each strand $\times$ number of strands

Q. Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a. At point B, the wqivalent force and couple are, respectiely.

1. F ($\leftarrow$) and $3\sqrt{3}Fa$ (clockwise)
2. F ($\to$) and zero
3. F ($\leftarrow$) and $\sqrt{3}Fa$ (counter clockwise)
4. F ($\to$) and $3\sqrt{3}Fa$ (counter clockwise)

Q. A ball of mass 0.1 kg, initially at rest, dropped from height of 1m. 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

Q. A truss hinged at A and supported on rollers and D is loaded as shown in the figure below.The force in member BC is

1. 6.6

Q. A shell is fired from a cannon. At the instant the shell is just 3 m/s, while the barrel is swimming upwards with a constant angular velocity of 2 rad/s. The magnitude of the absolute velocity of the shell is

1. $3\frac{m}{s}$
2. $4\frac{m}{s}$
3. $5\frac{m}{s}$
4. $7\frac{m}{s}$

Q. 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

Q. A single-plate clutch has a friction disc with inner and outer radii of 20 mm and 40 mm respectively. The friction lining in the disc is made in such a way that the coefficient of friction $\mu$ varies radially as $\mu$ = 0.01 r, where r is in mm. The clutch needs to transmit a friction torque of 18.85 kN mm. As per uniform pressure theory the pressure (in MPa) on the disc is

1. 0.5