Moment of inertia of a squares of side b about an axis through its centre of gravity, is
b3/4
b4/12
b4/3
b4/8
Correct Answer :
B. b4/12
Related Questions
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
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
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
A particle is dropped from the top of a tower 60 m high and another is projected upwards from the foot of the tower to meet the first particle at a height of 15.9 m. The velocity of projection of the second particle is
16 m/sec
18 m/sec
20 m/sec
22 m/sec
If the radius of the earth is 600 km the height of a mountain above sea level at the top of which a beat seconds pendulum at sea level, looses 27 seconds a day, is
500 metres
1000 metres
1500 metres
2000 metres
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
The velocity of a moving body, is
A vector quantity
A scalar quantity
A constant quantity
None of these
A rigid body is in a stable equilibrium if the application of any force
Can raise the CG of the body but cannot lower it
Tends to lower the CG of the body
Neither raises nor lowers the CG of the body
None of above
A weight of 100 kg is supported by a string whose ends are attached to pegs A and B at the same level shown in below figure. The tension in the string is 
50 kg
75 kg
100 kg
120 kg
The motion of a particle moving with S.H.M. from an extremity to the other, constitutes
Half an oscillation
One full oscillation
Two oscillations
None of these
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%
The angle of friction is:
The ratio of the friction and the normal reaction
The force of friction when the body is in motion
The angle between the normal reaction and the resultant of normal reaction and limiting friction
The force of friction at which the body is just about to move
The acceleration of a particle moving along the circumference of a circle with a uniform speed, is directed
Radially
Tangentially at that point
Away from the centre
Towards the centre
If g1 and g2 are the gravitational accelerations on two mountains A and B respectively, the weight of a body when transported from A to B will be multiplied by
g1
g2
g1/g2
g2/g1
On a ladder resisting on a smooth ground and leaning against a rough vertical wall, the force of friction acts
Towards the wall at its upper end
Away from the wall at its upper end
Upwards at its upper end
Downwards at its upper end
To double the period of oscillation of a simple pendulum
The mass of its bob should be doubled
The mass of its bob should be quadrupled
Its length should be quadrupled
Its length should be doubled
Which one of the following statements is true?
The tangent of the angle of friction is equal to coefficient of friction
The angle of repose is equal to angle of friction
The tangent of the angle of repose is equal to coefficient of friction
All the above
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
If the gravitational acceleration at any place is doubled, the weight of a body, will
Be reduced to half
Be doubled
Not be affected
None of these
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
A system of coplanar forces acting on a rigid body can be reduced to
One force only
One couple only
One force and one couple only
None of the above
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
Pick up the correct statement from the following. A rubber ball when strikes a wall rebounds but a lead ball of same mass and velocity when strikes the same wall, falls down
Rubber and lead balls undergo equal changes in momentum
Change in momentum suffered by lead ball is less that of rubber ball
Momentum of rubber ball is less than that of lead ball
None of these
If a body moves in such a way that its velocity increases by equal amount in equal intervals of time, it is said to be moving with
A uniform retardation
A uniform acceleration
A variable acceleration
A variable retardation
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
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
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 shell of mass 100 kg travelling with a velocity of 10 m/sec breaks into two equal pieces during an explosion which provides an extra kinetic energy of 20000 Joules. If the pieces continue to move in the same direction as before, then the speed of the faster one must be
20 m/sec
30 m/sec
40 m/sec
50 m/sec
A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec²)
1/4
1/3
1/2
1/5
The necessary condition of equilibrium of a body is:
Algebraic sum of horizontal components of all the forces must be zero
Algebraic sum of vertical components of all the forces must be zero
Algebraic sum of the moments of the forces about a point must be zero
All (a), (b) and (c)