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)
Correct Answer :
D. (ii) and (iv)
Related Questions
A cable loaded with 0.5 tonne per horizontal metre span is stretched between supports in the same horizontal line 400 m apart. If central dip is 20 m, the minimum tension in the cable, will be
200 tonnes at the centre
500 tonnes at the centre
200 tonnes at the right support
200 tonnes at the left support
If two bodies of masses M1 and M2(M1 > M2) are connected by alight inextensible string passing over a smooth pulley, the tension in the string, will be given by
T = g(M1 - M2)/(M1 + M2)
T = g(M1 + M2)/(M1 × M2)
T = g(M2 - M1)/(M1 + M2)
T = g(M2 + M1)/(M2 - M1)
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
A 49 kg lady stands on a spring scale in an elevator. During the first 5 sec, starting from rest, the scale reads 69 kg. The velocity of the elevator will be
10 m/sec
15 m/sec
20 m/sec
25 m/sec
The height at which the end of a rope of length l should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is
¾ l
½ l
l/√2
2/√3 l
A flywheel of moment of inertia 20 kgm is acted upon by a tangential force of 5 N at 2 m from its axis, for 3 seconds. The increase in angular velocity in radian per second is
1/2
3/2
2
3
A particle of mass 2 kg executes simple harmonic motion of frequency 6/71 Hz and amplitude 0.25 m. Its maximum kinetic energy is
4.5 J
9.0 J
12.0 J
18.0 J
Impulse can be obtained from a
Force-displacement diagram
Force-time diagram
Velocity-time diagram
Velocity-displacement diagram
Three forces which act on a rigid body to keep it in equilibrium. The forces must be coplanar and
Concurrent
Parallel
Concurrent parallel
None of these
If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is
Zero
Maximum
Minimum
None of these
In a lifting machine with efficiency 60%, an effort of 200 N is required to raise a load of 6 kN. The velocity ratio of the machine is
30
50
60
80
Minimum potential energy of a system will be in the position of
Stable equilibrium
Unstable equilibrium
Neutral equilibrium
All of the above
Total no of instantaneous centres of a machine having n links, is
n/2
n
(n - 1)
n (n - 1)/2
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
Time required to stop a car moving with a velocity 20 m/sec within a distance of 40 m, is
2 sec
3 sec
4 sec
5 sec
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
At a given instant ship A is travelling at 6 km/h due east and ship B is travelling at 8 km/h due north. The velocity of B relative to A is
7 km/hrs
2 km/hrs
1 km/hrs
10 km/hrs
A stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad/sec. The tension in the string is,
5 N
10 N
15 N
25 N
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
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 velocity ratio of the differential wheel and axle is
R/r1 - r2
2R/r1
3R/r1 - r2
2R/r1 + r2
For a simple pendulum, the period of one oscillation is
2π √(l/2g)
2π √(2g/l)
2π √(l/g)
2π √(g/2l)
For a simple pendulum, time period for a beat, is
π √(l/g)
π √(2l/g)
π √(g/2l)
π √(l/2g)
The unit of moments in M.K.S system, is
kg.m
kg/m2
kg/sec2
kg/sec
The unit of Moment of Inertia of a body, is
m
m2
m3
m4
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
The Centre of gravity of a 10 × 15 × 5 cm T-section from its bottom, is
7.5 cm
5.0 cm
8.75 cm
7.85 cm
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
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
A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The velocity ratio of the lifting machine is
50
55
60
65