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

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

Bissoy MCQ
#Mechanical Engineering #Theory of Machine

Related Questions

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 $${\text{m}}{\omega ^2}{\text{r}}\frac{{\cos2\theta }}{{\text{n}}}$$
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 $$\frac{{\omega \,\cos\theta }}{{{{\left( {{{\text{n}}^2} - {{\sin }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
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 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
A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$  = Angular velocity of precession of the axis of spin)
A $$\frac{1}{2}I{\omega ^2}$$
B $$I{\omega ^2}$$
C $$\frac{1}{2}I\omega \omega {\text{P}}$$
D $$I\omega \omega {\text{P}}$$
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 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 $${\omega ^2}{\text{r}} \times \frac{{\text{n}}}{{{\text{n}} - 1}}$$
Radius of circle center 0 is 3 times the radius of circle center C. Angle ACB -A angle POQ. If the shaded are of circle C is 2 then what is the area of then shaded part of circleO?
A 36
B 9
C 12
D 18

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