The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to
log r
r
r²
1/r Where r is the distance of the particle from centre of the earth
Correct Answer :
C. r²
Related Questions
The mechanical advantage of an ideal machine is 100. For moving the local through 2 m, the effort moves through
0.02 m
2 m
2.5 m
20 m
For a particle moving with a simple harmonic motion, the frequency is
Directly proportional to periodic time
Inversely proportional to periodic time
Inversely proportional to its angular velocity
Directly proportional to its angular velocity
The shape of a suspended cable under its own weight, is
Parabolic
Circular
Catenary
Elliptical
A ball moving with a velocity of 5 m/sec impinges a fixed plane at an angle of 45° and its direction after impact is equally inclined to the line of impact. If the coefficient of restitution is 0.5, the velocity of the ball after impact will be
0.5 m/sec
1.5 m/sec
2.5 m/sec
3.5 m/sec
For a non-concurrent force system to be in equilibrium
Only the closure of force polygon is sufficient
Only the closure of funicular polygon is sufficient
Both force polygon and funicular polygon must close
None of the above
A retarding force on a body does not
Change the motion of the body
Retard the motion of the body
Introduce the motion of the body
None of these
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
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
The following factor affects the orbit of a satellite up to an altitude of 720 km from the earth's surface
Uneven distribution of the gravitational field
Gravity of the sun and the moon
Aerodynamic forces
None of these
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
A stone is thrown vertically upwards with a vertical velocity of 49 m/sec. It returns to the ground in
5 sec
8 sec
10 sec
20 sec
The beam shown in below figure is supported by a hinge at A and a roller at B. The reaction RA of the hinged support A of the beam, is 
10.8 t
10.6 t
10.4 t
10.2 t
If two forces acting at a point are in equilibrium, they must be equal in magnitude and their line of action must be along
The same line in the same sense
The same line in opposite sense
The perpendicular to both the lines
None of these
When a body in equilibrium undergoes an infinitely small displacement, work imagined to be done, is known as
Imaginary work
Negative work
Virtual work
None of these
The rate of change of displacement of a body with respect to its surrounding, is known
Velocity
Acceleration
Speed
None of these
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 phenomenon of collision of two elastic bodies takes place because bodies
Immediately after collision come momentarily to rest
Tend to compress each other till they are compressed maximum possible
Attempt to regain its original shape due to their elasticities
All the above
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
Parallelogram Law of Forces states, if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by
Its longer side
Its shorter side
The diagonal of the parallelogram which does not pass through the point of intersection of the forces
The diagonal of the parallelogram which passes through the point of intersection of the forces
The unit of Moment of Inertia of a body, is
m
m2
m3
m4
Periodic time of body moving with simple harmonic motion, is
Directly proportional to its angular velocity
Directly proportional to the square of its angular velocity
Inversely proportional to the square of its angular velocity
Inversely proportional to its angular velocity
In simple harmonic motion, acceleration of a particle is proportional to
Rate of change of velocity
Displacement
Velocity
Direction
If l is the span of a light suspension bridge whos each cable carries total weight (w) and the central dip is y, the horizontal pull at each support, is
wl/4y
wl/8y
wl/2y
wl
If the resultant of two forces P and Q acting at an angle θ makes an angle α with P, then tan α equals
P sin θ/P - Q cos θ
Q sin θ/P + Q cos θ
P sin θ/P + Q tan θ
Q sin θ/P + Q sin θ
The C.G. of a hemisphere from its base measured along the vertical radius is at a distance of
4R/3π
3R/8
3πR/4
8R/3
M.I. of solid sphere, is
Mr2
½ Mr2
Mr2
πr4/2
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
A square hole is made in a circular lamina, the diagonal of the square is equal to the radius of the circle as shown in below figure the shift in the centre of gravity is 
r (π - 0.75)/(π - 0.5)
r (π - 0.25)/(π - 0.75)
r (π - 0.5)/(π - 0.75)
r (π - 0.5)/(π - 0.25)
A particle executes a simple harmonic motion. While passing through the mean position, the particle possesses
Maximum kinetic energy and minimum potential energy
Maximum kinetic energy and maximum potential energy
Minimum kinetic energy and maximum potential energy
Minimum kinetic, energy and minimum potential energy
The torque produced by a force depends on (i) The magnitude of the force (ii) The direction of the force (iii) The point of application of the force relative to origin The correct answer is
Only (i)
Both (i) and (ii)
Both (i) and (iii)
All (i), (ii) and (iii)