A body of weight w placed on an inclined plane is acted upon by a force P parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is θ and angle of friction is φ, the minimum value of P, is
w sin (φ - θ)/cos φ
w sin (θ - φ)/cos φ
w cos (θ + φ)/cos φ
w sinθ cos(θ - φ)/sin φ
Correct Answer :
B. w sin (θ - φ)/cos φ
Related Questions
If α and u are angle of projection and initial velocity of a projectile respectively, the total time of flight, is given by
T = u sin 2α/g
T = u sin²α/g
T = u sin²α/2g
T = 2u sinα/g
Parallelogram Law of Forces states, if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by
Its longer side
Its shorter side
The diagonal of the parallelogram which does not pass through the point of intersection of the forces
The diagonal of the parallelogram which passes through the point of intersection of the forces
A particle moves in a straight line and its position is defined by the equation x = 6 t² - t3 where t is expressed in seconds and x in meters. The maximum velocity during the motion is
6 m/sec
12 m/sec
24 m/sec
48 m/sec
For a given velocity of a projectile, the range is maximum when the angle of projection is
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45°
90°
0°
If three rigid rods are hinged together to form a triangle and are given rotary as well as translatory motion, the number of instantaneous centres of the triangle, will be
1
2
3
4
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b3h/12
bh3/3
bh3/36
bh3/2
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229.34 cm4
329.34 cm4
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If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of the restitution between the ball and floor, is
0.25
0.50
0.67
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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)
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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
Maximum efficiency of a screw jack for the angle of friction θ, is
sin θ/(1 + sin θ)
(1 - sin θ)/sin θ
(1 + sin θ)/(1 - sin θ)
(1 - sin θ)/(1 + sin θ)
Centre of gravity of a thin hollow cone lies on the axis of symmetry at a height of
One-half of the total height above base
One-third of the total height above base
One-fourth of the total height above base
None of these
In a simple screw jack, the pitch of the screw is 9 mm and length of the handle operating the screw is 45 cm. The velocity ratio of the system is
1.5
5
25
314
A particle moving with a simple harmonic motion, attains its maximum velocity when it passes
The extreme point of the oscillation
Through the mean position
Through a point at half amplitude
None of these
A body of weight w placed on an inclined plane is acted upon by a force P parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is θ and angle of friction is φ, the minimum value of P, is
w sin (φ - θ)/cos φ
w sin (θ - φ)/cos φ
w cos (θ + φ)/cos φ
w sinθ cos(θ - φ)/sin φ
The locus of the instantaneous centre of a moving rigid body, is
Straight line
Involute
Centroid
Spiral
The following is in unstable equilibrium
A uniform solid cone resting on a generator on a smooth horizontal plane
A uniform solid cone resting on its base on a horizontal plane
A solid cube resting on one edge
A satellite encircling the earth
A funicular polygon cannot be made to pass through
One specified point
Two specified points
Three specified points
More than three specified points
A smooth cylinder lying on its convex surface remains
In stable equilibrium
In unstable equilibrium
In neutral equilibrium
Out of equilibrium
A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a
Parabola
Catenary
Cycloid
Ellipse
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
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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 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
Free body diagram is an
Isolated joint with only body forces acting on it
Isolated joint with internal forces acting on it
Isolated joint with all the forces, internal as well as external, acting on it
None of the above
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Rotates
Moves with variable velocity in a straight line
Moves along a curved path
Does not move at all
Joule is the unit of
Power
Impulse
Work
Momentum
The condition of equilibrium for any system of forces in a plane is
That polygon of forces must close
That resultant couple must be zero
Both (A) and (B)
None of the above
Pick up the incorrect statement from the following. In a simple harmonic motion
Velocity is maximum at its mean position
Velocity is minimum at the end of the stroke
Acceleration is minimum at the end of the stroke
Acceleration is zero at the mean position
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πd4/12
πd4/16
πd4/24
πd4/32
A satellite moves in its orbit around the earth due to
Gravitational force
Centripetal force
Centrifugal force
None of these