Lami's theorem states that
Three forces acting at a point are always in equilibrium
If three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium
Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
Three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
Correct Answer :
C. Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
Related Questions
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
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°
The resultant of two forces P and Q acting at an angle θ, is
P2 + Q2 + 2P sin θ
P2 + Q2 + 2PQ cos θ
P2 + Q2 + 2PQ tan θ
√(P2 + Q2 + 2PQ cos θ)
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
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)
A marble ball is rolled on a smooth floor of a room to hit a wall. If the time taken by the ball in returning to the point of projection is twice the time taken in reaching the wall, the coefficient of restitution between the ball and the wall, is
0.25
0.50
0.75
1.0
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
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
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
To attain the synchronous orbit, the launch of a satellite, is done from a place
On equator
On 30° latitude
On 45° latitude
On the poles
A body A of mass 6.6 kg which is lying on a horizontal platform 4.5 m from its edge is connected to the end of a light string whose other end is supporting a body of mass 3.2 kg as shown in below figure. If the friction between the platform and the body A is 1/3, the acceleration is 
0.5 m/sec2
0.75 m/sec2
1.00 m/sec2
1.25 m/sec2
A particle moves along a straight line such that distance x traversed in t seconds is given by x = t2(t + 1), the acceleration of the particle, will be
3t3 - 2t
3t2 + 2t
6t - 2
6t + 2
A retarding force on a body does not
Change the motion of the body
Retard the motion of the body
Introduce the motion of the body
None of these
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
If a particle moves with a uniform angular velocity ω radians/sec along the circumference of a circle of radius r, the equation for the velocity of the particle, is
v = ω √(y² - r²)
y = ω √(y - r)
v = ω √(r² + y²)
v = ω √(r² - y²)
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)
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
M.I. of solid sphere, is
Mr2
½ Mr2
Mr2
πr4/2
A uniform pyramid and a uniform prism of same height lie with their base on the surface. Which is more stable?
Pyramid
Prism
Both equally stable
None of the above
According to Kennedy's theorem, if three bodies have plane motions, their instantaneous centres lie on
A point
A straight line
Two straight lines
A triangle
When a body slides down an inclined surface, the acceleration (f) of the body, is given by
f = g
f = g sin θ
f = g cos θ
f = g tan θ
Instantaneous center is at infinity when the angular velocity is
Constant
Zero
Maximum
Minimum
Minimum pull in a suspended cable with supports at two ends is equal to
Horizontal thrust
Support reactions
Resultant of horizontal thrust and support reaction
Half the weight of the cable
A projectile is thrown at an angle α to the horizontal with velocity v. It will have the maximum centripetal acceleration
At the start
At the top of the trajectory
As it strikes the ground
Elsewhere
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
If the kinetic energy and potential energy of a simple harmonic oscillator of amplitude A are both equal to half the total energy, then the displacement is equal to
A
A/2
A/√2
A√2
Minimum potential energy of a system will be in the position of
Stable equilibrium
Unstable equilibrium
Neutral equilibrium
All of the above
Periodic time of body moving with simple harmonic motion, is
Directly proportional to its angular velocity
Directly proportional to the square of its angular velocity
Inversely proportional to the square of its angular velocity
Inversely proportional to its angular velocity
Select the correct statement
The body centrode rolls on the space centrode
The space centrode rolls on the body centrode
Both body and space centrodes may role on each other
The body centrode never touches space centrode
A square hole is made in a circular lamina, the diagonal of the square is equal to the radius of the circle as shown in below figure the shift in the centre of gravity is 
r (π - 0.75)/(π - 0.5)
r (π - 0.25)/(π - 0.75)
r (π - 0.5)/(π - 0.75)
r (π - 0.5)/(π - 0.25)