Applied Mechanics and Graphic Statics MCQs

Question 1

A string of length 90 cm is fastened to two points ‘A’ and ‘B’ at the same level 60 cm apart. A ring weighing 120 g is slided on the string. A horizontal force ‘P’ is applied to the ring such that it is in equilibrium vertically below ‘B’. The value of ‘P’ is:

Accepted Answer

80 g

Answer

40 g

Answer

60 g

Answer

100 g

Question 2

A body of weight w placed on an inclined plane is acted upon by a force P parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is $$	heta $$ and angle of friction is $$\varphi $$, the minimum value of P, is

Accepted Answer

$$\frac{{{	ext{w}}\sin \left( {	heta - \varphi } ight)}}{{\cos \varphi }}$$

Answer

$$\frac{{{	ext{w}}\sin \left( {\varphi - 	heta } ight)}}{{\cos \varphi }}$$

Answer

$$\frac{{{	ext{w}}\cos \left( {	heta + \varphi } ight)}}{{\cos \varphi }}$$

Answer

$$\frac{{{	ext{w}}\sin 	heta \cos\left( {	heta - \varphi } ight)}}{{\sin\varphi }}$$

Question 3

If the linear velocity of a point on the rim of a wheel of 10 m diameter, is 50 m/sec, its angular velocity will be

Accepted Answer

5 rad/sec

Answer

20 rad/sec

Answer

15 rad/sec

Answer

10 rad/sec

Question 4

The centre of gravity of a trapezoidal dam section whose top width is a, bottom width is b and the vertical side is a, from its vertical face is

Accepted Answer

$$\frac{{{{	ext{a}}^2} + {	ext{ab}} + {{	ext{b}}^2}}}{{3\left( {{	ext{a}} + {	ext{b}}} ight)}}$$

Answer

$$\frac{{{{	ext{b}}^2} + {	ext{bc}} + {{	ext{c}}^2}}}{{3\left( {{	ext{b}} + {	ext{c}}} ight)}}$$

Answer

$$\frac{{{{	ext{a}}^2} + {	ext{ac}} + {{	ext{c}}^2}}}{{3\left( {{	ext{a}} + {	ext{c}}} ight)}}$$

Answer

None of these

Question 5

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

Accepted Answer

Change in momentum suffered by lead ball is less that of rubber ball

Answer

Rubber and lead balls undergo equal changes in momentum

Answer

Momentum of rubber ball is less than that of lead ball

Answer

None of these

Question 6

If two forces of 3 kg and 4 kg act at right angles to each other, their resultant force will be equal to

Accepted Answer

5 kg

Answer

7 kg

Answer

1 kg

Answer

None of these

Question 7

The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\frac{1}{2}$$, the velocities of separation of the balls will be equal to

Accepted Answer

Original velocity in the opposite direction

Answer

Original velocity in the same direction

Answer

Half the original velocity in the same direction

Answer

Half the original velocity in the opposite direction

Question 8

When a body of mass M1 is hanging freely and another of mass M2 lying on a smooth inclined plane ($$\alpha $$) 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

Accepted Answer

$$\frac{{{	ext{g}}\left( {{{	ext{M}}_1} - {{	ext{M}}_2}\sin \alpha } ight)}}{{{{	ext{M}}_1} + {{	ext{M}}_2}}}{	ext{m/se}}{{	ext{c}}^2}$$

Answer

$$\frac{{{	ext{g}}\left( {{{	ext{M}}_1} + {{	ext{M}}_2}\sin \alpha } ight)}}{{{{	ext{M}}_1} + {{	ext{M}}_2}}}{	ext{m/sec}}$$

Answer

$$\frac{{{	ext{g}}\left( {{{	ext{M}}_2} + {{	ext{M}}_1}\sin \alpha } ight)}}{{{{	ext{M}}_1} + {{	ext{M}}_2}}}{	ext{m/se}}{{	ext{c}}^2}$$

Answer

$$\frac{{{	ext{g}}\left( {{{	ext{M}}_2} 	imes {{	ext{M}}_1}\sin \alpha } ight)}}{{{{	ext{M}}_2} - {{	ext{M}}_1}}}{	ext{m/se}}{{	ext{c}}^2}$$

Question 9

If two bodies of masses M1 and M2(M1 > M2) are connected by alight inextensible string passing over a smooth pulley, the tension in the string, will be given by

Accepted Answer

$${	ext{T}} = \frac{{{	ext{g}}\left( {{{	ext{M}}_1} - {{	ext{M}}_2}} ight)}}{{{{	ext{M}}_1} + {{	ext{M}}_2}}}$$

Answer

$${	ext{T}} = \frac{{{	ext{g}}\left( {{{	ext{M}}_1} + {{	ext{M}}_2}} ight)}}{{{{	ext{M}}_1} 	imes {{	ext{M}}_2}}}$$

Answer

$${	ext{T}} = \frac{{{	ext{g}}\left( {{{	ext{M}}_2} - {{	ext{M}}_1}} ight)}}{{{{	ext{M}}_1} + {{	ext{M}}_2}}}$$

Answer

$${	ext{T}} = \frac{{{	ext{g}}\left( {{{	ext{M}}_2} + {{	ext{M}}_1}} ight)}}{{{{	ext{M}}_2} - {{	ext{M}}_1}}}$$