In a reciprocating steam engine, when the crank has turned from inner dead center through an angle $$\theta $$, the angular velocity of the connecting rod is given by

The velocity of piston in a reciprocating steam engine is given by (where $$\omega $$ = Angular velocity of crank, r = Radius of crank pin circle, $$\theta $$ = Angle turned by crank from inner dead center and n = Ratio of length of connecting rod to the radius of crank)

A

$$\omega {\text{r}}\left( {\sin \theta + \frac{{\sin 2\theta }}{{\text{n}}}} \right)$$

B

$$\omega {\text{r}}\left( {\cos\theta + \frac{{\cos2\theta }}{{\text{n}}}} \right)$$

C

$${\omega ^2}{\text{r}}\left( {\sin \theta + \frac{{\sin 2\theta }}{{\text{n}}}} \right)$$

D

$${\omega ^2}{\text{r}}\left( {\cos\theta + \frac{{\cos2\theta }}{{\text{n}}}} \right)$$

The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, $$\omega $$ = Angular speed of crank, r = Radius of crank, $$\theta $$ = Angle of inclination of crank with the line of stroke and n = Ratio of the length of connecting rod to radius of crank)

A

$${\text{m}}{\omega ^2}{\text{r}}\sin \theta $$

B

$${\text{m}}{\omega ^2}{\text{r}}\cos \theta $$

C

$${\text{m}}{\omega ^2}{\text{r}}\frac{{\sin 2\theta }}{{\text{n}}}$$

D

$${\text{m}}{\omega ^2}{\text{r}}\frac{{\cos2\theta }}{{\text{n}}}$$

The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, $$\omega $$ = Angular speed of crank, r = Radius of crank, $$\theta $$ = Angle of inclination of crank with the line of stroke and n = Ratio of the length of connecting rod to radius of crank)

A

$${\text{m}}{\omega ^2}{\text{r}}\sin \theta $$

B

$${\text{m}}{\omega ^2}{\text{r}}\cos \theta $$

C

$${\text{m}}{\omega ^2}{\text{r}}\frac{{\sin 2\theta }}{{\text{n}}}$$

D

$${\text{m}}{\omega ^2}{\text{r}}\frac{{\cos2\theta }}{{\text{n}}}$$

The tractive force in a locomotive with two cylinders is given by (where c = Fraction of reciprocating parts per cylinder, m = Mass of reciprocating parts, $$\omega $$ = Angular speed of crank, r = Radius of crank and $$\theta $$ = Angle of inclination of crank to the line of stroke)

A

$${\text{m}}{\omega ^2}{\text{r}}\cos \theta $$

B

$${\text{cm}}{\omega ^2}{\text{r}}\sin \theta $$

C

$$\left( {1 - {\text{c}}} \right){\text{m}}{\omega ^2}{\text{r}}\left( {\cos \theta - \sin \theta } \right)$$

D

$${\text{m}}{\omega ^2}{\text{r}}\left( {\cos \theta - \sin \theta } \right)$$

When the crank is at the inner dead center, in a reciprocating steam engine, then the acceleration of the piston will be

A

$${\omega ^2}{\text{r}} \times \frac{{{\text{n}} + 1}}{{\text{n}}}$$

B

$${\omega ^2}{\text{r}} \times \frac{{{\text{n}} - 1}}{{\text{n}}}$$

C

$${\omega ^2}{\text{r}} \times \frac{{\text{n}}}{{{\text{n}} + 1}}$$

D

$${\omega ^2}{\text{r}} \times \frac{{\text{n}}}{{{\text{n}} - 1}}$$

When the primary direct crank of a reciprocating engine makes an angle of $$\theta $$ with the line of stroke, then the secondary direct crank will make an angle of _________ with the line of stroke.

A

$$\frac{\theta }{2}$$

B

$$\theta $$

C

$$2\theta $$

D

$$4\theta $$

When the crank is at the inner dead centre, in a reciprocating steam engine, then the velocity of the piston will be

A

Minimum

B

Zero

C

Maximum

D

None of these

When the crank is at the outer dead centre, in a reciprocating steam engine, then the acceleration of the piston will be

A

$${\omega ^2}{\text{r}} \times \frac{{{\text{n}} + 1}}{{\text{n}}}$$

B

$${\omega ^2}{\text{r}} \times \frac{{{\text{n}} - 1}}{{\text{n}}}$$

C

$${\omega ^2}{\text{r}} \times \frac{{\text{n}}}{{{\text{n}} + 1}}$$

D

$${\omega ^2}{\text{r}} \times \frac{{\text{n}}}{{{\text{n}} - 1}}$$

The values of velocity and acceleration of piston at near dead center for a slider-crank mechanism will be

A

0, and more than co2r

B

0, and less than coV

C

0, 0

D

cor, 0

The velocity of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by (where $$\omega $$ = Angular velocity of the cam shaft)

A

$$\omega \left( {{{\text{r}}_1}{{\text{r}}_2}} \right)\sin \theta $$

B

$$\omega \left( {{{\text{r}}_1} + {{\text{r}}_2}} \right)\sin \theta \sec 2\theta $$

C

$$\omega \left( {{{\text{r}}_1}{{\text{r}}_2}} \right)\cos \theta $$

D

$$\omega \left( {{{\text{r}}_1} + {{\text{r}}_2}} \right)\cos \theta \,{\text{cosec2}}\theta $$

In a reciprocating steam engine, when the crank has turned from inner dead center through an angle $$\theta $$, the angular velocity of the connecting rod is given by

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