A ball moving with a velocity of 5 m/sec impinges a fixed plane at an angle of 45° and its direction after impact is equally inclined to the line of impact. If the coefficient of restitution is 0.5, the velocity of the ball after impact will be
0.5 m/sec
1.5 m/sec
2.5 m/sec
3.5 m/sec
Correct Answer :
C. 2.5 m/sec
Related Questions
A bullet weighing 10 gm moves with a velocity of l km/sec. Its kinetic energy is (i) 5000 Nm (ii) 5000 kg.m (iii) 5000 J The correct answer is
Only (ii)
Both (i) and (iii)
Both (ii) and (iii)
All (i), (ii) and (iii)
If l is the span of a light suspension bridge whos each cable carries total weight (w) and the central dip is y, the horizontal pull at each support, is
wl/4y
wl/8y
wl/2y
wl
Pick up the correct statement from the following:
If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities
If a sphere impinges directly on an equal sphere which is at rest, then a fraction ½(1 - e2) the original kinetic energy is lost by the impact
If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles
All the above
A disc of mass 4 kg, radius 0.5 m and moment of inertia 3 kgm² rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is
50 J
150 J
200 J
400 J
A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if
Floor is smooth and the wall is rough
Floor is rough and the wall is smooth
Floor and wall both are smooth surfaces
Floor and wall both are rough surfaces
Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m/sec and 1 m/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is
2/3
1/5
3/5
1/3
The velocity ratio of an inclined plane of inclination θ with horizontal for lifting a load is
sin θ
cos θ
tan θ
cosec θ
The C.G. of a hemisphere from its base measured along the vertical radius is at a distance of
4R/3π
3R/8
3πR/4
8R/3
Cartesian form of the equation of catenary is
y = c cosh x/c
y = c sinh x/c
y = c tan x/c
y = c sin x/c
In SI units, the units of force and energy are respectively
Newton and watt
Dyne and erg
Newton and joule
kg wt and joule
The intrinsic equation of catenary is
S = c tan ψ
y = c cosh x/c
y = c cosh ψ
y = c sinh ψ
For a simple pendulum, the period of one oscillation is
2π √(l/2g)
2π √(2g/l)
2π √(l/g)
2π √(g/2l)
The velocity of a moving body, is
A vector quantity
A scalar quantity
A constant quantity
None of these
A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous center of rotation when the ladder starts slipping? (i) 1.0 in from the wall (ii) 1.732 m from the wall (iii) 1.0 m above the floor (iv) 1.732 m above the floor The correct answer is
(i) and (iii)
(i) and (iv)
(ii) and (iii)
(ii) and (iv)
Rate of change of angular momentum is equal to
Force
Torque
Linear momentum
Impulse
The acceleration of a train starting from rest at any instant is 1/6(V + 1) m/sec² where V is the velocity of the train in m/sec. The train will attain a velocity of 36 km/hour after travelling a distance of
2000 m
2100 m
2200 m
2300 m
A stone is whirled in a vertical circle, the tension in the string, is maximum
When the string is horizontal
When the stone is at the highest position
When the stone is at the lowest position
At all the positions
One end of a light string 4 m in length is fixed to a point on a smooth wall and the other end fastened to a point on the surface of a smooth sphere of diameter 2.25 m and of weight 100 kg. The reaction between the sphere and the wall of the arrangement made is
102.5 kg
105.5 kg
108.5 kg
110 kg
A funicular polygon cannot be made to pass through
One specified point
Two specified points
Three specified points
More than three specified points
The motion of a particle is described by the relation x = t2- 10t + 30, where x is in metres and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be
Zero
30 m
50 m
60 m
On a ladder resting on a rough ground and leaning against a smooth vertical wall, the force of friction acts
Downwards at its upper end
Upwards at its upper end
Perpendicular to the wall at its upper end
Zero at its upper end
A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan1 x, where x is
3/4
4/5
5/3
3/5
A pilot flies a small plane in a vertical loop of radius r. At the top of its trajectory he experiences weightlessness. If the acceleration due to gravity is g, the speed of the plane at the top of its trajectory would be
Zero
Infinite
gr
2gr
The resultant of the forces acting on a body will be zero if the body
Rotates
Moves with variable velocity in a straight line
Moves along a curved path
Does not move at all
The diagram showing the point of application and line of action of forces in their plane is called
Vector diagram
Space diagram
Force diagram
Funicular diagram
According to Law of Triangle of Forces
Three forces acting at a point, can be rep-resented by the sides of a triangle, each side being in proportion to the force
Three forces acting along the sides of a triangle are always in equilibrium
If three forces acting on a, point can be represented in magnitude and direction, by the sides of a triangle taken in order, these will be in equilibrium
If the forces acting on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant will be represented in magnitude and direction by the third side of the triangle, taken in opposite order
The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is
1/4
1/2
3/4
2
The ends of a string weighing w/metre are attached to two points at the same horizontal level. If the central dip is very small, the horizontal tension of the string throughout is
wl/4d
wl²/4d
wl²/8d
wl²/16d
The following is not a law of static friction:
The force of friction always acts in a direction opposite to that in which the body tends to move
The force of friction is dependent upon the area of contact
The force of friction depends upon the roughness of the surface
The magnitude of the limiting friction bears a constant ratio to the normal reaction between two surfaces
A rigid body is in a stable equilibrium if the application of any force
Can raise the CG of the body but cannot lower it
Tends to lower the CG of the body
Neither raises nor lowers the CG of the body
None of above