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

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

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

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 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

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

গরম বাতাসে পরিপূর্ণ M ভরের একটি বেলুন (থ্রডি সহ) পৃথিবীর দিকে খুব ত্বরণ a তে নেমে আসছে। ঝুড়ি থেকে কি পরিমান m ভর ফেলে দিলে বেলুনটি উপরের দিকে একই খুব ত্বরন a- তে উঠে যাবে ? সকল ক্ষেত্রে বেলুনটির আয়তন একই ছিল বলে ধরে নেওয়া হলো। (g = অভিকর্ষীয় ত্বরন)(A hot air balloon with a bucket is descending towards the earth with a constant acceleration a. The combined mass of the balloon and bucket is M. What mass m from the bucket should be released so that the balloon starts ascending up with the same acceleration a? Consider the volume of the balloon remains constant at all the time. (g=acceleration due to gravity))

A

m=2ag+aM

B

m=g+a2M

C

m=2ag M

D

m=M2a(g+a)

E

m=ag+M

The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line

A

joining the corresponding points

B

perpendicular to line

C

at 450 to line

D

none of the mentioned

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

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

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

For the same length of stroke and speed of crankshaft, the piston speed for a double acting steam engine is _________ the piston speed of single acting steam engine.

A

Equal to

B

Twice

C

Three times

D

Four times

When the piston is at T.D.C., the volume above the piston in the combustion chamber is the

A

Clearance volume

B

Cylinder volume

C

Exhaust volume

D

None of these

The lower cylindrical portion of the piston which improves piston cooling performance is called

A

Piston crown

B

Connecting rod

C

Piston pin boss

D

Piston skirt

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

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