μ is coefficient of friction. A wheeled vehicle travelling on a circular level track will slip and overturn simultaneously if the ratio of its wheel distance to the height of its centroid, is
μ
2μ
3μ
½μ
Correct Answer :
B. 2μ
Related Questions
The member which does not carry zero force in the structure shown in below figure, is
ED
DC
BC
BD
A trolley wire weighs 1 kg per metre length. The ends of the wire are attached to two poles 20 m apart. If the horizontal tension is 1000 kg, the central dip of the cable is
2 cm
3 cm
4 cm
5 cm
The reaction RB of the roller support B of the beam shown in below figure is 
10.8 t
10.6 t
10.4 t
10.2 t
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
The condition for a lifting machine to be reversible is that its efficiency should be
Less than 50%
More than 50%
More than 66.67%
Equal to 100%
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
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
Total no of instantaneous centres of a machine having n links, is
n/2
n
(n - 1)
n (n - 1)/2
A string of length 90 cm is fastened to two points A and B at the same level 60 cm apart. A ring weighing 120 g is slided on the string. A horizontal force P is applied to the ring such that it is in equilibrium vertically below B. The value of P is:
40 g
60 g
80 g
100 g
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
If a spherical body is symmetrical about its perpendicular axes, the moment of inertia of the body about an axis passing through its centre of gravity as given by Routh's rule is obtained by dividing the product of the mass and the sum of the squares of two semi-axes by n. Where, n is
2
3
4
5
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
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)
A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec. The work required to stop the hoop is
2 J
4 J
6 J
8 J
The equation of motion of a particle starting from rest along a straight line is x = t3 - 3t2+ 5. The ratio of the accelerations after 5 sec and 3 sec will be
2
3
4
5
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
Principle of Transmissibility of Forces states that, when a force acts upon a body, its effect is
Maximum if it acts at the centre of gravity of the body
Different at different points on its line of
Same at every point on its line of action
Minimum if it acts at the C.G. of the body
A bullet weighing 200 g is fired horizontally with a velocity of 25 m/sec from a gun carried on a carriage which together with the gun weighs 100 kg. The velocity of recoil of the gun, will be
0.01 m/sec
0.05 m/sec
1.00 m/sec
1.5 m/see
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)
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
A sphere is resting on two planes BA and BC which are inclined at 45° and 60° respectively with the horizontal. The reaction on the plane BA will be
Less than that on BC
More than that of BC
Equal to that on BC
None of these
A ball of mass 1 kg moving with a velocity of 2 m/sec collides a stationary ball of mass 2 kg and comes to rest after impact. The velocity of the second ball after impact will be
Zero
0.5 m/sec
1.0 m/sec
2.0 m/sec
Pick up the incorrect statement from the following:
The C.G. of a circle is at its centre
The C.G. of a triangle is at the intersection of its medians
The C.G. of a rectangle is at the intersection of its diagonals
The C.G. of a semicircle is at a distance of r/2 from the centre
If the angle of projection is double the angle of inclination (α) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be
½ cos α
½ sin α
½ tan α
2 cos α
For a self-locking machine, the efficiency should be
Less than 60%
50 %
More than 50%
None of these
Energy may be defined as
Power of doing work
Capacity of doing work
Rate of doing work
All the above
A train weighing 196 tonnes experiences a frictional resistance of 5 11/22 per tonne. The speed of the train at the top of a down gradient 1 in 78.4 is 36 km/hour. The speed of the train after running 1 km down the slope, is
5 √10 m/sec
10 √5 m/sec
5 √3 m/sec
3 √5 m/sec
The tension in a cable supporting a lift
Is more when the lift is moving downwards
Is less when the lift is moving upwards
Remains constant whether its moves downwards or upwards
Is less when the lift is moving downwards
If G is the Gauge of track, v is velocity of the moving vehicle, g is the acceleration due to gravity and r is the radius of a circular path, the required super elevation is
gv²/Gr
Gr²/gr
Gr²/gv²
Gv²/gv
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