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
Correct Answer :
D. 5
Related Questions
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
A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is
n rpm
n/2 rpm
n/4 rpm
2n rpm
The following is not a law of static friction:
The force of friction always acts in a direction opposite to that in which the body tends to move
The force of friction is dependent upon the area of contact
The force of friction depends upon the roughness of the surface
The magnitude of the limiting friction bears a constant ratio to the normal reaction between two surfaces
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 moment of inertia of a triangular section (base b, height h) about centroidal axis parallel to the base, is
b3h/12
bh3/3
bh3/36
bh3/2
For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is
α = π/4 - β/2
α = π/2 + β/2
α = β/2 - π/2
α = π/4 - β/2
The length of a Second's pendulum, is
99.0 cm
99.4 cm
100 cm
101 cm
The intrinsic equation of catenary is
S = c tan ψ
y = c cosh x/c
y = c cosh ψ
y = c sinh ψ
From a circular plate of a diameter 6 cm is cut out a circle whose diameter is equal to the radius of the plate. The C.G. of the remainder from the centre of circular plate is at a distance of
2.0 cm
1.5 cm
1.0 cm
0.5 cm
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
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
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
Joule is the unit of
Power
Impulse
Work
Momentum
The moment of inertia of a hollow circular section whose external diameter is 8 cm and internal diameter is 6 cm, about centroidal axis, is
437.5 cm4
337.5 cm4
237.5 cm4
137.5 cm4
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
A Second's pendulum gains 2 minutes a day. To make it to keep correct time its length
Must be decreased
Must be increased
Is not changed but weight of the bob is increased
Is not changed but weight of the bob is decreased
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
The velocity of a body fallen from height h, on reaching the ground is given by
v = 2gh
v = 2gh2
v = √(2gh)
v = 1/√(2gh)
In the structure shown in below figure, the member which carries zero force, is 
AB
BC
BE
All the above
The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be
30°
45°
60°
75°
A uniform rod 9 m long weighing 40 kg is pivoted at a point 2 m from one end where a weight of 120 kg is suspended. The required force acting at the end in a direction perpendicular to rod to keep it equilibrium, at an inclination 60° with horizontal, is
40 kg
60 kg
10 kg
100 kg
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
Williot-Mohr diagram is used to determine deflection in
Trusses only
Beam only
Rigid frames only
Any type of structure
Two shots fired simultaneously from the top and bottom of a vertical tower with elevations of 30° and 45° respectively strike a target simultaneously. If horizontal distance of the target from the tower is 1000 m, the height of the tower is
350 m
375 m
400 m
425 m
A satellite goes on moving along its orbit round the earth due to
Gravitational force
Centrifugal force
Centripetal force
None of these
If a body is acted upon by a number of coplanar non-concurrent forces, it may
Rotate about itself without moving
Move in any one direction
Move in any one direction rotating about itself
All the above
The member which does not carry zero force in the structure shown in below figure, is
ED
DC
BC
BD
The C.G. of a thin hollow cone of height h, above its base lies on the axis, at a height of
h/3
h/4
2h/3
3h/4
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
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