In locomotives, the ratio of the connecting rod length to me crank radius is kept very large in order to

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 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 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

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

A cylindrical rod of iron, whose height is equal to its radius ,is melted and cast into spherical balls whose radius is half the radius of the rod. find the number of balls.

A

3

B

4

C

5

D

6

A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod . Find the number of balls.

A

2

B

3

C

4

D

6

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

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

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

$$4\theta $$

The number of centers in a crank driven slider crank mechanism is

A

0

B

2

C

4

D

6

In order to have a connecting rod equally strong in buckling about X-axis and Y-axis, the moment of inertia about X-axis should be __________ the moment of inertia about Y-axis.

A

Equal to

B

Twice

C

Three times

D

Four times

In locomotives, the ratio of the connecting rod length to me crank radius is kept very large in order to

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