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

A $$\frac{{\omega \,\sin \theta }}{{{{\left( {{{\text{n}}^2} - {{\sin }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
B $$\frac{{\omega \,\cos\theta }}{{{{\left( {{{\text{n}}^2} - {{\cos }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
C $$\frac{{\omega \,\sin \theta }}{{{{\left( {{{\text{n}}^2} - {{\cos }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
D $$\frac{{\omega \,\cos\theta }}{{{{\left( {{{\text{n}}^2} - {{\sin }^2}\theta } \right)}^{\frac{1}{2}}}}}$$

Correct Answer: $$\frac{{\omega \,\cos\theta }}{{{{\left( {{{\text{n}}^2} - {{\sin }^2}\theta } \right)}^{\frac{1}{2}}}}}$$

Bissoy MCQ
#Mechanical Engineering #Theory of Machine

Related Questions

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

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