Applied Mechanics And Graphic Statics MCQ

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• The velocity ratio of the differential wheel and axle is
  ক

  $$\frac{{\text{R}}}{{{{\text{r}}_1} - {{\text{r}}_2}}}$$

  খ

  $$\frac{{2{\text{R}}}}{{{{\text{r}}_1}}}$$

  গ

  $$\frac{{3{\text{R}}}}{{{{\text{r}}_1} - {{\text{r}}_2}}}$$

  ঘ

  $$\frac{{2{\text{R}}}}{{{{\text{r}}_1} + {{\text{r}}_2}}}$$
• The practical units of work, is
  ক

  Erg

  খ

  Joule

  গ

  Newton

  ঘ

  Dyne
• A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If ‘r’ is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be
  ক

  $$\frac{{{\text{r}}\left( {\pi + 0.25} \right)}}{{\pi - 0.5}}$$

  খ

  $$\frac{{{\text{r}}\left( {\pi - 0.5} \right)}}{{\pi + 0.25}}$$

  গ

  $$\frac{{{\text{r}}\left( {\pi - 0.25} \right)}}{{\pi - 0.5}}$$

  ঘ

  $$\frac{{{\text{r}}\left( {\pi + 0.25} \right)}}{{\pi + 0.5}}$$
• A particle moving with a simple harmonic motion, attains its maximum velocity when it passes
  ক

  The extreme point of the oscillation

  খ

  Through the mean position

  গ

  Through a point at half amplitude

  ঘ

  None of these
• A geo-stationary satellite is one which orbits the earth with a velocity of rotation of
  ক

  Moon

  খ

  Earth

  গ

  Sun

  ঘ

  Pole
• The shape of a suspended cable under its own weight, is
  ক

  Parabolic

  খ

  Circular

  গ

  Catenary

  ঘ

  Elliptical
• The graphical method of determining the forces in the members of a truss is based on
  ক

  Method of joint

  খ

  Method of section

  গ

  Either method

  ঘ

  None of the two methods
• A stone is whirled in a vertical circle, the tension in the string, is maximum
  ক

  When the string is horizontal

  খ

  When the stone is at the highest position

  গ

  When the stone is at the lowest position

  ঘ

  At all the positions
• The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to (where r is the distance of’the particle from centre of the earth)
  ক

  log r

  খ

  r

  গ

  r²

  ঘ

  $$\frac{1}{{\text{r}}}$$
• Which of the following represents the state of neutral equilibrium?
  ক

  A cube resting on one edge

  খ

  A smooth cylinder lying on a curved surface

  গ

  A smooth cylinder lying on a convex surface

  ঘ

  None of the above
• A rigid body is in a stable equilibrium if the application of any force
  ক

  Can raise the CG of the body but cannot lower it

  খ

  Tends to lower the CG of the body

  গ

  Neither raises nor lowers the CG of the body

  ঘ

  None of above
• The angle of projection at which the horizontal range and maximum height of a projectile are equal to
  ক

  36°

  খ

  45°

  গ

  56°

  ঘ

  76°
• The unit of Moment of Inertia of a body, is
  ক

  m

  খ

  m²

  গ

  m³

  ঘ

  m⁴
• The motion of a particle moving with S.H.M. from an extremity to the other, constitutes
  ক

  Half an oscillation

  খ

  One full oscillation

  গ

  Two oscillations

  ঘ

  None of these
• If the resultant of two forces has the same magnitude as either of the force, then the angle between the two forces is
  ক

  30°

  খ

  45°

  গ

  60°

  ঘ

  120°
• A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a
  ক

  Parabola

  খ

  Catenary

  গ

  Cycloid

  ঘ

  Ellipse
• A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first?
  ক

  Sphere with greater rotational energy at bottom than cylinder

  খ

  Sphere with lesser rotational energy at bottom than cylinder

  গ

  Cylinder with greater rotational energy at bottom than sphere

  ঘ

  Both reach the bottom simultaneously with equal rotational energy at bottom
• The following is in unstable equilibrium
  ক

  A uniform solid cone resting on a generator on a smooth horizontal plane

  খ

  A uniform solid cone resting on its base on a horizontal plane

  গ

  A solid cube resting on one edge

  ঘ

  A satellite encircling the earth
• The centre of gravity of a homogeneous body is the point at which the whole
  ক

  Volume of the body is assumed to be concentrated

  খ

  Area of the surface of the body is assumed to be concentrated

  গ

  Weight of the body is assumed to be concentrated

  ঘ

  All the above
• Three forces which act on a rigid body to keep it in equilibrium. The forces must be coplanar and
  ক

  Concurrent

  খ

  Parallel

  গ

  Concurrent parallel

  ঘ

  None of these
• The tension in a cable supporting a lift
  ক

  Is more when the lift is moving downwards

  খ

  Is less when the lift is moving upwards

  গ

  Remains constant whether its moves downwards or upwards

  ঘ

  Is less when the lift is moving downwards
• The apparent weight of a man in a moving lift is less than his real weight when it is going down with
  ক

  Uniform speed

  খ

  An acceleration

  গ

  Linear momentum

  ঘ

  Retardation
• Centre of gravity of a thin hollow cone lies on the axis of symmetry at a height of
  ক

  One-half of the total height above base

  খ

  One-third of the total height above base

  গ

  One-fourth of the total height above base

  ঘ

  None of these
• The C.G. of a right circular cone lies on its axis of symmetry at a height of
  ক

  $$\frac{{\text{h}}}{2}$$

  খ

  $$\frac{{\text{h}}}{3}$$

  গ

  $$\frac{{\text{h}}}{4}$$

  ঘ

  $$\frac{{\text{h}}}{5}$$
• The velocity of a body fallen from height ‘h’, on reaching the ground is given by
  ক

  v = 2gh

  খ

  v = 2gh²

  গ

  $${\text{v}} = \sqrt {2{\text{gh}}} $$

  ঘ

  $${\text{v}} = \frac{1}{{\sqrt {2{\text{gh}}} }}$$
• The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be
  ক

  $$\frac{{\sin \left( {\alpha + \beta } \right)}}{{\sin \left( {\alpha - \beta } \right)}}$$

  খ

  $$\frac{{\sin \left( {\alpha - \beta } \right)}}{{\sin \left( {\alpha + \beta } \right)}}$$

  গ

  $$\frac{{\cos \left( {\alpha - \beta } \right)}}{{\cos \left( {\alpha + \beta } \right)}}$$

  ঘ

  $$\frac{{\tan \left( {\alpha - \beta } \right)}}{{\tan \left( {\alpha + \beta } \right)}}$$
• Periodic time of body moving with simple harmonic motion, is
  ক

  Directly proportional to its angular velocity

  খ

  Directly proportional to the square of its angular velocity

  গ

  Inversely proportional to the square of its angular velocity

  ঘ

  Inversely proportional to its angular velocity
• The dimensions of centrifugal force are
  ক

  M1 L2 T2

  খ

  M’L’T1

  গ

  M’L’T2

  ঘ

  M’L-‘T2
• Moment of inertia of a squares of side ‘b’ about an axis through its centre of gravity, is
  ক

  $$\frac{{{{\text{b}}^3}}}{4}$$

  খ

  $$\frac{{{{\text{b}}^4}}}{{12}}$$

  গ

  $$\frac{{{{\text{b}}^4}}}{3}$$

  ঘ

  $$\frac{{{{\text{b}}^4}}}{8}$$
• When a body falls freely under gravitational force, it possesses
  ক

  Maximum weight

  খ

  Minimum weight

  গ

  No weight

  ঘ

  No effect on its weight