The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where $$\delta $$ = Static deflection of a simply supported shaft due to the point load)

The natural frequency of free transverse vibrations due to uniformly distributed load acting over a simply supported shaft is (where $$\delta {\text{S}}$$ = Static deflection of simply supported shaft due to uniformly distributed load)

A

$$\frac{{0.4985}}{{\sqrt {\delta {\text{S}}} }}$$

B

$$\frac{{0.5615}}{{\sqrt {\delta {\text{S}}} }}$$

C

$$\frac{{0.571}}{{\sqrt {\delta {\text{S}}} }}$$

D

$$\frac{{0.6253}}{{\sqrt {\delta {\text{S}}} }}$$

Consider the following remarks pertaining to the irrotational flow: 1. The Laplace equation of stream function $\frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {y^2}}} = 0$ must be satisfied for the flow to be potential. 2. The Laplace equation for the velocity potential $\frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {y^2}}} = 0$ must be satisfied to fulfil the orate . of mass conservation i.e continuity equation.. Which of the above statements is/are correct?

A

1 only

B

Both 1 and 2

C

2 only

D

Neither 1 or 2

The natural frequency of free longitudinal vibrations is equal to (where m = Mass of the body, s = Stiffness of the body and $$\delta $$ = Static deflection of the body)

A

$$\frac{1}{{2\pi }} \times \sqrt {\frac{{\text{s}}}{{\text{m}}}} $$

B

$$\frac{1}{{2\pi }} \times \sqrt {\frac{{\text{g}}}{\delta }} $$

C

$$\frac{{0.4985}}{{\sqrt \delta }}$$

D

Any one of these

There are two beams of equal length L and a load P is acting on centre of both beams. One of them is simply supported at both ends while the other one is fixed at both ends. Deflection of centre of simply supported beam will be __________ times that of defection of centre of fixed beam.

A

1

B

2

C

3

D

4

The natural frequency of free torsional vibrations of a shaft is equal to (where q = Torsional stiffness of the shaft and $$I$$ = Mass moment of inertia of the disc attached at the end of a shaft)

A

$$2\pi \sqrt {\frac{{\text{q}}}{I}} $$

B

$$2\pi \sqrt {{\text{q}}I} $$

C

$$\frac{1}{{2\pi }}\sqrt {\frac{{\text{q}}}{I}} $$

D

$$\frac{1}{{2\pi }}$$

Consider the following statements in connection with deflection-type and null-type instruments: 1. Null-type instruments are more accurate than the deflection-type ones. 2. Null-type of instrument can be highly sensitive compared to a deflection-type instrument. 3. Under dynamic conditions, null-type instruments are less preferred to deflection-type instruments. 4. Response is faster in null-type instruments as compared to deflection-type instruments. Which of the above statements are correct?

A

1, 2 and 3

B

1, 2 and 4

C

1, 3 and 4

D

2, 3 and 4

How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is metres to the east of point 'T'. Point 'M' is metres to the east of point 'Z'. Point 'R' is metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.

A

Statement (I) and (III) are independently sufficient to answer the question.

B

Statement (I) and (II) are together required to answer the question.

C

Statement (I) alone is sufficient to answer the question while statement (II) is not sufficient to answer the question.

D

Statement (II) alone is sufficient to answer (I) is not sufficient to answer the question.

Which of the following statements regarding static methods are correct?
1. Static methods are difficult to maintain, because you can not change their implementation.
2. Static methods can be called using an object reference to an object of the class in which this method is defined.
3. Static methods are always public, because they are defined at class-level.
4. Static methods do not have direct access to non-static methods which are defined inside the same class.

A

1 and 2

B

2 and 4

C

3 and 4

D

1 and 3

In SDT, what are the boundary conditions for a plate that is simply supported if ф represents the rotation of the transverse normal about an in-plane axis and w is the transverse deflection?

A

w=0,$\frac{\partial w}{\partial n}$=0

B

w=0,ф=0

C

w=0,$\frac{\partial w}{\partial n}$≠0

D

w=0, Mnn=0

Point A is 3m in the north of point B. Point D is 2m in the east of point E. Point F is 9m in the west of point G. Point C is 4m in the west of point B. Point C is 3m in the south of point D. Point F is 5m in the south of point E. Point H is 5m in the north of point G. What is the shortest distance between point H and point A?

A

5m

B

4m

C

3m

D

6m

The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where $$\delta $$ = Static deflection of a simply supported shaft due to the point load)

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