A spherical body is symmetrical about its perpendicular axis. According to Routh's rule, the moment of inertia of a body about an axis passing through its centre of gravity is (where, M = Mass of the body, and S = Sum of the squares of the two semi-axes.)
MS/3
MS/4
MS/5
None of these
Correct Answer :
C. MS/5
Related Questions
The acceleration of a particle moving with simple harmonic motion, at any instant is given by
ω.y
ω2.y
ω2/y
ω3.y
The moment of inertia of a thin rod of mass m and length l, about an axis through its centre of gravity and perpendicular to its length is
ml2/4
ml2/ 6
ml2/8
ml2/12
When the lift is moving upwards with some acceleration, the pressure exerted by a man is __________ to its acceleration.
Directly proportional
Inversely proportional
Cube root
None of these
Which of the following do not have identical dimensions?
Momentum and impulse
Torque and energy
Torque and work
Moment of a force and angular momentum.
Which of the following is the locus of a point that moves in such a manner that its distance from a fixed point is equal to its distance from a fixed line multiplied by a constant greater than one
Ellipse
Hyperbola
Parabola
Circle
The coefficient of friction depends on
Area of contact
Shape of surfaces
Strength of surfaces
Nature of surface
Two like parallel forces are acting at a distance of 24 mm apart and their resultant is 20 N. It the line of action of the resultant is 6 mm from any given force, the two forces are
15 N and 5 N
20 N and 5 N
15 N and 15 N
None of these
A force acting on a body may
Change its motion
Balance the other forces acting on it
Retard its motion
All of the above
A circular hole of 50 mm diameter is cut out from a circular disc of 100 mm diameter as shown in the below figure. The centre of gravity of the section will lie 
In the shaded area
In the hole
At O
None of these
According to Newton's first law of motion,
Everybody continues in its state of rest or of uniform motion, in a straight line, unless it is acted upon by some external force
The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts
To every action, there is always an equal and opposite reaction
None of the above
The maximum velocity of a particle moving with simple harmonic motion is
ω
ωr
ω2r
ω/r
The C.G. of a right circular solid cone of height h lies at the following distance from the base
h/2
J/3
h/6
h/4
The centre of gravity of a quadrant of a circle lies along its central radius (r) at a distance of
0.5r
0.6 r
0.7 r
0.8 r
Moment of inertia of a rectangular section having width (b) and depth (d) about an axis passing through its C.G. and parallel to the width (b), is
db³/12
bd³/12
db³/36
bd³/36
A block of mass 20 kg lying on a rough horizontal plane is connected by a light string passing over a smooth pulley to another mass 5 kg, which can move freely in the Vertical direction, as shown in the below figure. The tension in the string will __________ with the increase in coefficient of friction. 
Increase
Decrease
Not be effected
None of these
A cable with a uniformly distributed load per horizontal meter run will take the following shape
Straight line
Parabola
Hyperbola
Elliptical
The moment of inertia of a thin disc of mass m and radius r, about an axis through its centre of gravity and perpendicular to the plane of the disc is
mr2/2
mr2/4
mr2/6
mr2/8
Three forces acting on a rigid body are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. The forces are equivalent to a couple whose moment is equal to
Area of the triangle
Twice the area of the triangle
Half the area of the triangle
None of these
In order to completely specify angular displacement by a vector, it must fix
Direction of the axis of rotation
Magnitude of angular displacement
Sense of angular displacement
All of these
The equivalent length of a simple pendulum which gives the same frequency as compound pendulum is
h/(kG² + h²)
(kG² + h²)/h
h²/(kG² + h²)
(kG² + h²)/h²
The wheels of a moving car possess
Potential energy only
Kinetic energy of translation only
Kinetic energy of rotation only
Kinetic energy of translation and rotation both
According to Lamis theorem
The three forces must be equal
The three forces must be at 120° to each other
The three forces must be in equilibrium
If the three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two
The law of the machine is (where P = Effort applied to lift the load, m = A constant which is equal to the slope of the line, W = Load lifted, and C = Another constant which represents the machine friction.)
P = mW - C
P = m/W + C
P = mW + C
P = C - mW
The maximum height of a projectile on a horizontal plane, is
u² sin²α/2g
u² cos²α/2g
u² sin²α/g
u² cos²α/g
Frictional force encountered after commencement of motion is called
Limiting friction
Kinematic friction
Frictional resistance
Dynamic friction
Which of the following are vector quantities?
Linear displacement
Linear velocity
Linear acceleration
All of these
The horizontal range of a projectile (R) is given by
R = u² cos2α/g
R = u² sin2α/g
R = u² cosα/g
R = u² sinα/g
The law of motion involved in the recoil of gun is
Newton's first law of motion
Newton's second law of motion
Newton's third law of motion
None of these
The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by (where r = Amplitude of motion, and y = Displacement of the particle from mean position.)
ω.√(y² - r²)
ω.√(r² - y²)
ω².√(y² - r²)
ω².√(r² - y²)
A number of forces acting at a point will be in equilibrium, if
All the forces are equally inclined
Sum of all the forces is zero
Sum of resolved parts in the vertical direction is zero (i.e. ΣV = 0)
None of these