One end of a light string 4 m in length is fixed to a point on a smooth wall and the other end fastened to a point on the surface of a smooth sphere of diameter 2.25 m and of weight 100 kg. The tension in the string is
17.5 kg
19.5 kg
22.5 kg
25 kg
Correct Answer :
C. 22.5 kg
Related Questions
A body is said to move with Simple Harmonic Motion if its acceleration, is
Always directed away from the centre, the point of reference
Proportional to the square of the distance from the point of reference
Proportional to the distance from the point of reference and directed towards it
Inversely proportion to the distance from the point of reference
The moment of inertia of the shaded portion of the area shown in below figure about the X-axis, is
229.34 cm4
329.34 cm4
429.34 cm4
529.34 cm4
If the horizontal range is 2.5 times the greatest height, the angle of projection of the projectile, is
57°
58°
59°
60°
μ is coefficient of friction. A wheeled vehicle travelling on a circular level track will slip and overturn simultaneously if the ratio of its wheel distance to the height of its centroid, is
μ
2μ
3μ
½μ
Two parallel forces 20 kg and 15 kg act. In order that the distance of the resultant from 20 kg force may be the same as that of the former resultant was from 15 kg, the 20 kg force is diminished by
5.5 kg
6.25 kg
8.75 kg
10.5 kg
A disc of mass 4 kg, radius 0.5 m and moment of inertia 3 kgm² rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is
50 J
150 J
200 J
400 J
Varingons theorem of moments states
Arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point
Algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point
Arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by
1 : 2
1 : 1
2 : 1
3 : 1
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
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)
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
The angular speed of a car while taking a circular turn of radius 100 m at 36 km/hour, is
0.1 radian/sec
1 radian/sec
100 radian/sec
1000 radian/sec
A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if
Floor is smooth and the wall is rough
Floor is rough and the wall is smooth
Floor and wall both are smooth surfaces
Floor and wall both are rough surfaces
The unit of force in C.G.S. system of units, is called
Dyne
Newton
Kg
All the above
Select the correct statement
The body centrode rolls on the space centrode
The space centrode rolls on the body centrode
Both body and space centrodes may role on each other
The body centrode never touches space centrode
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
Time of flight of a projectile on a horizontal plane, is
2u sinα/g
2u cosα/g
2u tanα/g
2u cotα/g
A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
Floor is smooth and wall is rough
Floor is rough and wall is smooth
Both floor and wall are rough
Both floor and wall are smooth
The reaction at the support D of the continuous beam ABCD, hinged at two points shown in below figure is 
1.6 t
1.6 t ↓
0.5 t
0.5 t ↓
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%
Maximum efficiency of a screw jack for the angle of friction θ, is
sin θ/(1 + sin θ)
(1 - sin θ)/sin θ
(1 + sin θ)/(1 - sin θ)
(1 - sin θ)/(1 + sin θ)
When a body of mass M1 is hanging freely and another of mass M2 lying on a smooth inclined plane(α) are connected by a light index tensile string passing over a smooth pulley, the acceleration of the body of mass M1, will be given by
g(M1 + M2 sin α)/(M1 + M2) m/sec
g(M1 - M2 sin α)/(M1 + M2) m/sec²
g(M2 + M1 sin α)/(M1 + M2) m/sec²
g(M2 × M1 sin α)/(M2 - M1) m/sec²
In a simple harmonic motion, the position of equilibrium is always
Stable
Unstable
Neutral
None of the above
In a lifting machine a weight of 5 kN is lifted through 200 mm by an effort of 0.1 kN moving through 15 m. The mechanical advantage and velocity ratio of the machine are respectively
50 and 75
75 and 50
75 and 75
50 and 50
When a body slides down an inclined surface, the acceleration (f) of the body, is given by
f = g
f = g sin θ
f = g cos θ
f = g tan θ
The centre of gravity of a plane lamina will not be at its geometrical centre if it is a
Circle
Equilateral triangle
Rectangle
Right angled triangle
For a self-locking machine, the efficiency should be
Less than 60%
50 %
More than 50%
None of these
If a set of given forces are such that their free vectors build a closed polygon, then
The resultant force and resultant couple are always zero
The resultant force is zero but resultant couple is not zero
The resultant force is zero but resultant couple may not be zero
The resultant force and resultant couple both may not be zero
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
Which of the following is a scalar quantity?
Energy
Momentum
Torque
Impulse