A point B on a rigid link AB moves with respect to A with angular velocity $$\omega $$ rad/s. The radial component of the acceleration of B with respect to A, is (where vBA = Linear velocity of B with respect to A)

For realizing a binary half-subtractor having two inputs A and B, the current set of logical expression for the outputs D (A minus B) and X (borrow) are 1. The difference output D = A̅B + AB̅ 2. The borrow output B = AB̅ Which of the above statements is/are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

In a crank and slotted lever type quick return mechanism, the link moves with an angular velocity of 20 rad/s, while the slider moves with the linear velocity of 1.5 m/s. The magnitude and direction of Coriolis component of acceleration with respect to angular velocity are

A

30 m/s2 and direction is such as to rotate slider velocity in the same sense as the angular velocity

B

30 m/s2 and direction is such as to rotate slider velocity in the opposite sense as the angular velocity

C

60 m/s2 and direction is such as to rotate slider velocity in the same sense as the angular velocity

D

60 m/s2 and direction is such as to rotate slider velocity in the opposite sense as the angular velocity.

The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity $${\omega _1}$$ rad/s in the clockwise direction and the link OB turns with angular velocity $${\omega _2}$$ rad/s in the anticlockwise direction, then the rubbing velocity at the pin joint O is (where r = Radius of the pin at O)

A

$${\omega _1}{\omega _2}{\text{r}}$$

B

$$\left( {{\omega _1} - {\omega _2}} \right){\text{r}}$$

C

$$\left( {{\omega _1} + {\omega _2}} \right){\text{r}}$$

D

$$\left( {{\omega _1} - {\omega _2}} \right)2{\text{r}}$$

The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity $${\omega _1}$$ rad/s in the clockwise direction and the link OB turns with angular velocity $${\omega _2}$$ rad/s in the clockwise direction, then the rubbing velocity at the pin joint O is (where r = Radius of the pin at O)

A

$${\omega _1}{\omega _2}{\text{r}}$$

B

$$\left( {{\omega _1} - {\omega _2}} \right){\text{r}}$$

C

$$\left( {{\omega _1} + {\omega _2}} \right){\text{r}}$$

D

$$\left( {{\omega _1} - {\omega _2}} \right)2{\text{r}}$$

A point B on a rigid link AB moves with respect to A with angular velocity $$\omega $$ rad/s. The total acceleration of B with respect to A will be equal to

A

Vector sum of radial component and Coriolis component

B

Vector sum of tangential component and Coriolis component

C

Vector sum of radial component and tangential component

D

Vector difference of radial component and tangential component

Two monochromatic waves having frequencies $$\omega $$ and $$\omega + \Delta \omega \left( {\Delta \omega \ll \omega } \right)$$ and corresponding wavelengths $$\lambda $$ and $$\lambda - \Delta \lambda \left( {\Delta \lambda \ll \lambda } \right)$$ of same polarization, travelling along X-axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by

A

$$\frac{{\omega \lambda }}{{2\pi }},\,\frac{{\Delta \omega {\lambda ^2}}}{{2\pi \Delta \lambda }}$$

B

$$\omega \lambda ,\,\frac{{\Delta \omega {\lambda ^2}}}{{\Delta \lambda }}$$

C

$$\frac{{\omega \Delta \lambda }}{{2\pi }},\,\frac{{\Delta \omega \Delta \lambda }}{{2\pi }}$$

D

$$\omega \Delta \lambda ,\,\omega \Delta \lambda $$

Coriolis component of acceleration depends on 1. angular velocity of the link 2. acceleration of the slider 3. angular acceleration of the link Which of the above is/are correct?

A

1 only

B

2 only

C

1 and 3

D

2 and 3

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.

A slider moves with uniform velocity on a revolving link of length r with angular velocity ω. The Coriolis acceleration component of a point on the slider relative to a coincident point on the link is equal to

A

ω parallel to the link

B

2ω perpendicular to the link

C

ω perpendicular to the link

D

2ω parallel to the link

A slider moves with uniform velocity v on a revolving link of length r with angular velocity of ω. The Coriolis acceleration component of a point on the slider relative to a coincident point on the link is equal to

A

2rω parallel to the link

B

2ωv perpendicular to the link

C

2rω perpendicular to the link

D

2ωv parallel to the link

A point B on a rigid link AB moves with respect to A with angular velocity $$\omega $$ rad/s. The radial component of the acceleration of B with respect to A, is (where vBA = Linear velocity of B with respect to A)

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