A rod 5 m in length is moving in a vertical plane. When it is inclined at 60° to horizontal, its lower end is moving horizontally at 3 m/sec and upper end is moving in vertical direction. The velocity of its upper end, is
0.5 m/sec
1.0 m/sec
1.5 m/sec
2.5 m/sec
Correct Answer :
B. 1.0 m/sec
Related Questions
A ball is dropped from a height of 16 m on a horizontal floor. If it rebounds to a height of 9 m after striking the floor, the coefficient of restitution between ball and floor is
1/4
2/3
3/4
4/3
A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being 1/3. The ball rebounds at the same angle. The fraction of its kinetic energy lost is
1/3
2/3
1/9
8/9
To avoid bending action at the base of a pier,
Suspension and anchor cables are kept at the same level
Suspension and anchor cables are fixed to pier top
Suspension cable and anchor cables are attached to a saddle mounted on rollers on top of the pier
None the these
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 gravitational force makes a satellite go round the earth in a circular orbit, if it is projected with an initial velocity of
8.04 km/sec at a height of 285 km
11.11 km/sec at a height of 37,400 km
11.26 km/sec, the satellite escapes the pull of the earth
All the above
A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
Floor is smooth and wall is rough
Floor is rough and wall is smooth
Both floor and wall are rough
Both floor and wall are smooth
A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan1 x, where x is (Assume g = 10 m/sec²)
3/8
1/2
9/5
5/8
The maximum velocity of a body vibrating with a simple harmonic motion of amplitude 150 mm and frequency 2 vibrations/sec, is
188.5 m/sec
18.85 m/sec
1.885 m/sec
0.18845 m/sec
Two particles have been projected at angles 64° and 45° to the horizontal. If the velocity of projection of first is 10 m/sec, the velocity of projection of the other for equal horizontal ranges is
9.3 m/sec
8.3 m/sec
7.3 m/sec
6.3 m/sec
Which of the following represents the state of neutral equilibrium?
A cube resting on one edge
A smooth cylinder lying on a curved surface
A smooth cylinder lying on a convex surface
None of the above
On a ladder resisting on a smooth ground and leaning against a rough vertical wall, the force of friction acts
Towards the wall at its upper end
Away from the wall at its upper end
Upwards at its upper end
Downwards at its upper end
A geo-stationary satellite is one which orbits the earth with a velocity of rotation of
Moon
Earth
Sun
Pole
The centre of gravity of a plane lamina will not be at its geometrical centre if it is a
Circle
Equilateral triangle
Rectangle
Right angled triangle
An ordinate in a funicular polygon represents
Shear force
Resultant force
Bending moment
Equilibrium
If α and u are the angle of projection and initial velocity of a projectile respectively, the horizontal range of the projectile, is
u² sin α/g
u² sin² α/g
u² sin α/2g
u² sin² α/2g
A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is
1.00 m/sec
1.57 m/sec
3.14 m/sec
6.28 m/sec
If a body is lying on a plane whose inclination with the horizontal is less than the angle of friction, then? (i) A force is required to move the body upwards (ii) A force is required to move the body downward (iii) The body will not be in equilibrium The correct answer is
Only (i)
Only (ii)
Both (i) and (ii)
Both (i) and (iii)
The angles between two forces to make their resultant a minimum and a maximum respectively are
0° and 90°
180° and 90°
90° and 180°
180° and 0°
A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec²)
1/4
1/3
1/2
1/5
The resolved part of the resultant of two forces inclined at an angle θ in a given direction is
Algebraic sum of the resolved parts of the forces in the direction
Arithmetical sum of the resolved parts of the forces in the direction
Difference of the forces multiplied by cosine θ°
Sum of the forces multiplied by the tangent θ°
If two equal forces of magnitude P act at an angle θ, their resultant, will be
P cos θ/2
2P sin θ/2
P tan θ/2
2P cos θ/2
Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis?
Disc with larger density
Disc with smaller density
Both discs will have same rotational inertia
None of the above
In simple harmonic motion, acceleration of a particle is proportional to
Rate of change of velocity
Displacement
Velocity
Direction
The equation of motion of a particle starting from rest along a straight line is x = t3 - 3l2 + 5. The ratio of the velocities after 5 sec and 3 sec will be
2
3
4
5
Periodic time of a particle moving with simple harmonic motion is the time taken by the particle for
Half oscillation
Quarter oscillation
Complete oscillation
None of these
The apparent weight of a man in a moving lift is less than his real weight when it is going down with
Uniform speed
An acceleration
Linear momentum
Retardation
The velocity of a moving body, is
A vector quantity
A scalar quantity
A constant quantity
None of these
The resultant of two forces acting at right angles is 5 kgf and if they act at an angle of 60°, it is 37 kgf. The magnitudes of the forces are:
2 kgf, 3 kgf
3 kgf, 4 kgf
4 kgf, 5 kgf
5 kgf, 3 kgf
Impulse can be obtained from a
Force-displacement diagram
Force-time diagram
Velocity-time diagram
Velocity-displacement diagram
If the angular distance, 0 = 2t3 - 3t², the angular acceleration at t = 1 sec. is
1 rad/sec²
4 rad/sec²
6 rad/sec²
12 rad/sec²