Engineering Mechanics
Exam Duration: 45 Mins Total Questions : 30
A particle slides down a smooth inclined plane of elevation 45° fixed in an elevator going up with an acceleration g. The base of incline has length L.The time taken by particle to reach the bottom is
- (a)
\(\sqrt{L\over g}\)
- (b)
\(\sqrt{2L\over g}\)
- (c)
\(\sqrt{L\over 2g}\)
- (d)
\(\sqrt{g\over L}\)
The tension in cable ABD is
- (a)
66.66 N
- (b)
70.7 N
- (c)
88 N
- (d)
None of these
Force in member AE is
- (a)
20.7 kN
- (b)
41.57 kN
- (c)
31.17 kN
- (d)
zero
The coefficient of static friction between the two blocks shown in figure is 11 and the table is smooth. What maximum horizontal force F can be applied to the block of mass M so that the blocks move together?
Given m = 2 kg, M = 4 kg, μ = 0.1 and g = 10 rn/s2
- (a)
6N
- (b)
8N
- (c)
4N
- (d)
10N
surface below the bigger block is smooth. The coefficient of friction between the blocks is μ. Find the minimum force F that can be applied in order to keep the smaller blocks at rest with respect to the bigger block.
- (a)
\({1-\mu\over 1+\mu}(M+2m)g\)
- (b)
\({1+\mu\over 1-\mu}(M+2m)g\)
- (c)
\(\left(1-\mu\over 1+\mu\right)Mg\)
- (d)
\(\left(1+\mu\over 1-\mu\right)Mg\)
All the surfaces shown in figure are assumed to be frictionless. The block of mass m slides on the prism which in turn slides backward on the horizontal surface. Find the acceleration of the smaller block with respect to the prism.
Given, M=2kg, m= 1kg, θ= 30°.
- (a)
\({10\over 3}m/s^2\)
- (b)
\({15\over 7}m/s^2\)
- (c)
\({20\over 3}m/s^2\)
- (d)
\({19\over 5}m/s^2\)
A steel wheel of 600mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in newton, necessary to roll the wheel along the rail is
- (a)
0.5
- (b)
5
- (c)
15
- (d)
150
The assembly shown in the figure is composed of two massless rods of length I with two particles, each of mass m. The natural frequency of this assembly for small oscillations is
- (a)
\(\sqrt{g/l}\)
- (b)
\(\sqrt{2g/(l\ cos\alpha)}\)
- (c)
\(\sqrt{g/(l\ cos\alpha)}\)
- (d)
\(\sqrt{g/(l\ cos\alpha)}\)
The 2 kg mass C moving horizontally to the right, with a velocity of 5 mis, strikes the 8 kg mass B at the lower end of the rigid massless rod AB. The rod is suspended from a frictionless hingeatA and is initially at rest. If the coefficient of restitution between mass C and B is one, the angular velocity of rod AB immediately after impact is
- (a)
0.50 rad/s
- (b)
0.75 rad/s
- (c)
0.25 rad/s
- (d)
0.625 rad/s
Three particles of masses 0.50 kg, 1.0 kg and 1.5 kg are placed at the three corners of a right-angled triangle of sides 3.0cm, 4.0cm and5.0cm as shown in figure below. Locate the centre of mass of the system.
- (a)
x = 1.3, y = 1.5
- (b)
x=4,y=3
- (c)
x = 0.9, y = 0.7
- (d)
x = 2, y = 1.5
A table with smooth horizontal surface is turning at an angular speed to about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance a from the centre. The speed of the particle with respect to the table (as its distance from the centre becomes L) is (if a =\({L\over\sqrt 2}\))
- (a)
\(ωL\over \sqrt2\)
- (b)
\(ωL\over 2\)
- (c)
- (d)
2ωL
- (e)
√2ωL
A block of mass m is pushed against a spring of spring constant k fixed at one end to a wall. The block can slide on a frictionless table as shown in figure. The natural length of the spring is La and it is compressed to half its natural length when the block is released. The velocity of the block (when x = L0) is
- (a)
\(\sqrt{m\over k}L_o\)
- (b)
\(\sqrt{m\over k}.{L_o\over2}\)
- (c)
\(\sqrt{m\over k}.{L_o}\)
- (d)
\(\sqrt{k\over 2m}.{L_o}\)
A sphere of mass m rolls without slipping on an inclined plane of inclination \(\theta\).For pure rolling which condition should be satisfied?
- (a)
\(\mu >{1\over7}tan\theta\)
- (b)
\(\mu >{3\over7}tan\theta\)
- (c)
\(\mu >{5\over7}tan\theta\)
- (d)
\(\mu >{2\over7}tan\theta\)
The coefficient of restitution of a perfectly plastic impact is
- (a)
zero
- (b)
1
- (c)
2
- (d)
infinite
There are two points P and Q on a planar rigid body. The relative velocity between the two points
- (a)
should always be along PQ
- (b)
can be oriented along any direction
- (c)
should always be perpendicular to PQ
- (d)
should be along QP when the body undergoes pure translation
A block weighing 981 Nis resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is Il = 0.2. A vertical cable attached to the block provides partial support as shown. Aman can pull horizontally with a force of 100 N. What will be the tension T (in newton) in the cable, if the man is just able to move the block to the right?
- (a)
176.2
- (b)
196.0
- (c)
481
- (d)
981.0
The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t3 + 2t. If v is the velocity and a is the acceleration of the particle in consistent units, the motion started with
- (a)
v = a, a = 0
- (b)
v = 0, a = 2
- (c)
v = 2, a = 0
- (d)
v = 2, a = 2
A simple pendulum of length 5 m with a bob of mass 1kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. The net force on the bob at the mean position is
- (a)
zero
- (b)
2.5N
- (c)
5N
- (d)
25N
In the arrangement shown in figure, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed.
Mass M moves upwards with a speed
- (a)
2u cos θ
- (b)
u/cos θ
- (c)
2u / cos θ
- (d)
u cosθ
The centre of awheel rolling on a plane surface moves with a speed vo. A particle on the rim of the wheel at the same level as the centre will be moving at speed
- (a)
zero
- (b)
v0
- (c)
v0
- (d)
\(\sqrt 2v_0\)
- (e)
2v0
A small body attached to one end of vertically hanging spring is performing SHM about its mean position with angular frequency (0 and apmplitude a. If at height Y from the main position, the body gets detached from the spring, the value of Y, so that height H attained by mass is (the body does not interact with the spring during its subsequent motion after detachment (aω2 > g) is
- (a)
\(2g\over ω^2\)
- (b)
\(g\over ω^2\)
- (c)
\(ω^2\over 2g\)
- (d)
\(ω^2\over g\)
A spherical ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (see figure). The smaller sphere A has a radius R and the space between the two spheres has a width d. The ball has a diameter very slightly less than d. All surfaces are frictionless. The ball is given a gentle push (towards the right in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by θ (shown in the figure).
The angle at which contact of ball is lost from sphere A is
- (a)
\(cosθ={2\over3}\)
- (b)
\(cosθ={1\over3}\)
- (c)
\(cosθ={1\over2}\)
- (d)
None of these
Three particles A, Band C, each of mass m are connected to each other by three massless rigid rods to form a rigid, equilateral triangular body of side 1. This body is placed on a horizontal frictionless table (X-Y plane) and is hinged to it at the point A so that it can move without friction about the vertical axis through A (see figure). The body is set into rotational motion on the table about A with a constant angular velocity co. The magnitude of the vertical force exerted by the hinge on the body is
- (a)
zero
- (b)
√3mω2l
- (c)
3mω2l
- (d)
mω2l
A particle of mass 10-2 kg is moving along the positive X-axis underthe influenceofaforceF(x) =- K/(2x2) where K = 10-2N-m2.Attimet=0, it isatx= 1.0mandits velocity is v = O.Its velocity, when it reaches x = 0.50 m, is
- (a)
1m/s
- (b)
zero
- (c)
2m/s
- (d)
0.5m/s
If a system is in equilibrium and the position of the system depends upon many independent variables, the principle of virtual work state that the partial derivatives of its total potential energy with respect to each of the independent variable must be
- (a)
-1.0
- (b)
zero
- (c)
1.0
- (d)
infinite
Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3, the lower book is pulled with a horizontal force F. The minimum value of Ffor which slip occurs between the two books is
- (a)
zero
- (b)
1.06 N
- (c)
5.74 N
- (d)
8.83 N
A shell is fired from a cannon. When, the shell isjust about to leave the barrel, its velocity relative to the barrel is 3 mis , while the barrel is swinging upwards with a constant angular velocity of 2 rad/s. The magnitude of the absolute velocity of the shell is
- (a)
3 m/s
- (b)
4 m/s
- (c)
5 m/s
- (d)
7 m/s
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 radius r of the hub and the reel mass m. Symbol g represents the acceleration due to gravity.
The linear acceleration of the reel is
- (a)
\(gr^2\over (r^2+k^2)\)
- (b)
\(gk^2\over (r^2+k^2)\)
- (c)
\(grk\over (r^2+k^2)\)
- (d)
\(mgr^2\over (r^2+k^2)\)
Bodies 1 and 2 shown in the figure have equal mass m. All surfaces are smooth. The value of force P required to prevent sliding of body 2 on body 1 is
- (a)
P= 2 mg
- (b)
P= √2mg
- (c)
P= 2√2mg
- (d)
P= mg
Mass M slides in a frictionless slot in the horizontal direction and the bob of mass m is hinged to mass M at C, through a rigid massless rod. This system is released from rest with θ = 300. At the instant when θ = 00, the velocities of m and M can be determined using the fact that, for the system (ie, m and M together)
- (a)
the linear momenta in X and Y directions are conserved but the energy is not conserved
- (b)
the linear momenta in X and Y directions are conserved and the energy is also conserved
- (c)
the linear momentum in X direction is conserved and the energy is also conserved
- (d)
the linear momentum in Y direction is conserved and the energy is also conserved