# Engineering Mechanics Online Test

A boy throws a ball horizontally with a velocity of 4 m/s at a height of 3.2 m above the ground. If the coefficient of restitution between the ball and the ground is 0.8, the velocity of ball at first rebound will be (Take g = 10 m/s2 )
4 m/s
6.4 m/s
7.5 m/s
10.4 m/s
A particle of mass 0.1 kg is moving at 2m/s towards another particle of mass 0.2 kg at 4 m/s. Upon collision, it reverses its direction but continues moving with the same speed. The coefficient of restitution is about
0.28
0.35
0.66
0.81
A sphere P impinges directly onto another identical sphere Q at rest. If the coefficient of restitution is 0.5, the ratio of velocities Vq/Vp after the impact would be
1 : 1
2 : 1
3 : 1
2 : 3
A ball impinges directly upon another similar ball at rest and itself comes to rest due to impact. During collision, half of the kinetic energy gets dissipated. The coefficient of restitution is
0.25
0.5
0.707
0.84
A marble ball is rolled on smooth floor of a room and hits the wall after 1 second. Subsequent upon rebound, it takes twice the time to reach the initial position from where it was rolled. The coefficient of restitution between the wall and ball is
0.25
0.50
0.75
1.0
A tennis ball is dropped onto a plane surface from height 1.0 meter. After rebound, the ball rises to 0.64 meter height. The coefficient of restitution is
0.64
0.8
0.97
0.51
For perfectly elastic bodies, the value of coefficient of restitution is
1
0.5 to 1
0 to 0.5
zero
The coefficient of restitution is defined on the basis of
velocity components along the line of impact only
velocity components normal to the line of impact
energies of bodies before and after the impact
impulses of recovery and deformation for either body
For the mass-pulley system depicted in Fig. 1.42, the mass m2 = 5 kg is placed on a smooth inclined plane of inclination a where as the mass m1 = 5 kg is hanging free. The acceleration of the system is 1.5 m/s2. If each mass is doubled, the acceleration will be
0.75 m/s2
1.5 m/s2
3.0 m/s2
A mass m1 hanging at the end of a string moves a mass m2 along the surface of a smooth table. If mass m2 on the table is doubled, the tension in the string is increased by one-half. The ratio m1/m2is
2/3
1/2
3/2
2
Two bodies P and Q have 50 N weights each. Body B is suspended from a spring balance whereas body Q is balanced in a physical balance. Both the balances are placed in an elevator which moves upwards with an acceleration g/2. Then:
weight of P increases and weight of Q decreases
weight of P increases and weight of Q remains the same
weight of P decrease and weight of Q remains the same
weight of P decreases and weight of Q increases
An elevator weighs 2500 kg, and is moving vertically downwards with a constant acceleration. Starting from rest, it travels a distance of 35 meters during an interval of 10 seconds. The tension produced in the cable would be approximately
2325 kgf
2575 kgf
2500 kgf
2750 kgf
/
1.25 m/s2
2 m/s2
8 m/s2
12 m/s2
A 5 kg sphere is accelerated upward by a string whose breaking strength is 200 N. The maximum value of acceleration with which the sphere can move without breaking the string is
10 m/s2
20 m/s2
30 m/s2
50 m/s2
The tension in the cable supporting a lift moving upwards is twice the tension when the lift moves downwards. The acceleration of the lift is equal to
g
g/2
g/3
g/4
The apparent weight of a man in a lift is less than the real weight when the lift is going down
freely
under the force of gravity
with some constant velocity
with some acceleration
A man stands on a spring weighing scale in a lift which carries him upwards with acceleration. The reading on the weighing scale will be
true weight of the man
lower than the true weight
greater than the true weight
zero
/
25 mkgf
40 mkgf
60 mkgf
75 mkgf
An engine delivers constant power while driving a vehicle along a straight, level and frictionless road. The distance traveled by the car in time t would be a function of
t1/2
t3/4
t3/2
t2
A rope weighing 0.5 kgf per metre run hangs from a drum for a height of 10 m. The work done in winding up the rope on the drum is
5 mkgf
10 mkgf
25 mkgf
50 mkgf
A uniform chain of mass m and length l lies on a smooth table such that one-fourth of its length is hanging vertically down over the edge of the table. The work done to pull the hanging part of the chain on the table is
mgl
mgl/4
mgl/8
mgl/32
A bullet of mass 0.03 kg moving with a speed of 400 m/s penetrates 1 cm into a fixed block of wood. The average by the wood on the bullet is
10 kN
20 kN
25 kN
30 kN
A constant force F = ( 20 i + 30 j + 10k) kJ moves a particle from position r1 = (10i + 20j) m to r2 = (10i + 20j + 30k) m The work done by the force in kJ is
zero kJ
300 kJ
800 kJ
1100 kJ
/
1.5 m/s
3.0 m/s
4.7 m/s
6.3 m/s
A force f acts for one second on a body of mass 1 kg moving with an initial velocity u. Then which of the following state
Body covers a distance (u + f/2)
Final velocity of the body is (u + f)
Change in kinetic energy of body is 1/2m f2
Momentum of the body increases of f
A 0.125 kg plastic ball collides head on with a 0.5 kg lead ball whose speed is three times that of plastic ball. At the instant of contact, the ratio of the magnitudes of force on the plastic ball, and that on the lead ball will be
1 : 1
3 : 1
4 : 1
12 : 1
A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments and each of mass m are found to move with a speed v, each in mutually perpendicular directions. The total energy released in the process of explosion is
mv2
3/2 mv2
m2
4 mv2
Consider a one-dimensional elastic collision between an incoming body A of mass m1 and a body B of mass m2 initially at rest. For body B to move with greatest kinetic energy after collision
m1>m2
m1 m1 = m2
body A should recoil after collision
A body of mass m moving with velocity v makes a head-on elastic collision with a stationary body of mass nm. The fraction of the incident energy transferred to the body at rest is
n/n+1
n/(n+1)2
2n/(n+1)2
4n/(n+1)2
The weight of a pile driver is 250 kg and it drops freely 10 m on the top of a pile weighing 1000 kg. If the pile is driven by 10 cm, the common velocity of the pile driver and the pile after the impact is (Take g= 9.8 m/s2.)
1.4 m/s
2.8 m/s
3.5 m/s
4.2 m/s
A body of mass m moving towards right with a constant velocity v hits another body of twice the mass moving towards left with half the velocity. If they stick together on collision, they will
come to rest
move towards right
move towards left
can come to rest or move in any direction depending upon magnitude of masses and their velocities
A body of mass m moving with a constant velocity v hits another body of the same mass moving with the same velocity but in the opposite direction and sticks to it. After this collision, the composite system will move with a velocity
zero
v/2
v
2v
A bullet of mass m1 and moving with velocity v1 strikes a wooden block of mass m2 lying on a frictionless surface and gets embedded into it. The final velocity of the system is
(m1 + m2) v1
m1/m1 + m2 v1
m1 + m2/m1 v1
m1/(m1 + m2) v1
A bomb of mass 20 kg explodes into two pieces of mass 5 kg and 15 kg. If velocity of first part is 300 m/s, the velocity of other part would be
zero
30 m/s
100 m/s
900 m/s
When a bullet is fired from a gun, it is recoiled in the backward direction. It is due to
impulse
inertia
conservation of momentum
conservation of energy
A ball of mass m and velocity v strikes a wall at right angles and rebounds with undiminished speed. During the time t of collision, average force exerted on the wall is
mv2/2
mv2/t
mv2/2t
2mv/t
An object moves along x-axis from x = 0 to x = 16 cm under the action of a force Fx = 24 – 3x ( x in cm ). Then
work done on the object will be 384 j
work done o the object will be zero
the potential energy of the object will be maximum at x = 8 cm
the object will oscillate about its mean position
A ball weighing 0.01 kg hits a hard surface vertically with a speed of 5 m/s and rebounds with the same speed. The ball remains in contact with the surface for 0.01 second. The average force exerted by the surface on the ball in Newton’s is
0.1
1.0
5.0
10.0
A 150 gm cricket ball moving at 20 m/s is caught by a player and the catching process is completed in 0.1 second. The force of blow exerted by the ball on the hands of player is
3 N
8 N
24 N
30 N
A body is moving with a velocity 1 m/s and a force F is needed to stop it within a certain distance. If the speed of the body becomes three times, the force needed to stop it within same distance would be
1.5 F
3 F
6 F
9 F
While launching a rocket of mass 2 * 104 kg, a force of 5 * 105 is applied for 20 seconds. The velocity attained by the rocket at the end of 20 seconds would be
350 m/s
500 m/s
750 m/s
900 m/s
A stationary object of 10 kg mass is acted upon by 20N force for 5 seconds. The object will attain a final velocity of
1 m/s
10 m/s
20 m/s
30 m/s
Two balls of mass 2 kg and 4 kg respectively are connected to the two ends of a spring. The balls are pressed together and placed on a smooth table. When released, the lighter ball moves with an acceleration of 2 m/s2. The acceleration of the heavier ball will be
0.5 m/s2
1 m/s2
2 m/s2
4 m/s2
A truck of mass 3000 kg is moving at 10 m/s and is acted upon two forces : a forward force of 1000 N due to engine and a retarding force of 400 N due to friction. The truck then gains speed at the rate
0.2 m/s2
0.02 m/s2
0.4 m/s2
0.33 m/s2
A body of mass 1 kg attains a velocity of 30 m/s from its rest position when a force of 6 N is applied to it. The time for which force acts on the body is
0.5 s
20.5 s
5 s
1.5 s
A man weighing 60 N jumps off a railway train running on horizontal rails at 20 km/hr with a packet weighing 100 N 10 his hand. The thrust of packet on his hand is
Zero
100 N
500 N
700 N
Which of the following statements is wrong?
impulse equals the change in momentum
action and reaction are equal and opposite and hence cancel each other
the momentum of a system of two bodies is conserved when there is no external force acting on either body
the work done on a particle must equal change in its kinetic energy.
Two different bodies of masses m2 and m2 are dropped from the same height. The ratio of their momentum at the ground is________
m2/m1
m1/m2
(m1/m2)1/2
(m1/m2)2
Two similar balls are allowed to fall from different heights h1 and h 2. The ratio of their linear moment at half of their heights will be
Two balls of same size, one of mass 10 kg and other of mass 20 kg, are dropped simultaneously from a tower. When the balls are 2 m above the ground, they will have the same:
acceleration
momentum
kinetic energy
potential energy
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paper has 50 questions which are required to be completed in an hours time approximately

Discussion

A sphere P impinges directly onto another identical sphere Q at rest. If the coefficient of restitution is 0.5, the ratio of velocities Vq/Vp after the impact would be

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Kalyan Sarkar
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