The efficiency of a screw jack is maximum, when (where $$\alpha $$ = Helix angle and $$\varphi $$ = Angle of friction)

The efficiency of a screw jack is maximum, when (where $$\alpha $$ = Helix angle and $$\varphi $$ = Angle of friction.)

A

$$\alpha = {45^ \circ } + \frac{\varphi }{2}$$

B

$$\alpha = {45^ \circ } - \frac{\varphi }{2}$$

C

$$\alpha = {90^ \circ } + \varphi $$

D

$$\alpha = {90^ \circ } - \varphi $$

Efficiency of a screw jack is given by (where $$\alpha $$ = Helix angle and $$\varphi $$ = Angle of friction.)

A

$$\frac{{\tan \left( {\alpha + \varphi } \right)}}{{\tan \alpha }}$$

B

$$\frac{{\tan \alpha }}{{\tan \left( {\alpha + \varphi } \right)}}$$

C

$$\frac{{\tan \left( {\alpha - \varphi } \right)}}{{\tan \alpha }}$$

D

None of these

In a screw jack, the effort required to lift the load W is given by (where $$\alpha $$ = Helix angle and $$\varphi $$ = Angle of friction)

A

$${\text{P}} = {\text{W}}\tan \left( {\alpha - \varphi } \right)$$

B

$${\text{P}} = {\text{W}}\tan \left( {\alpha + \varphi } \right)$$

C

$${\text{P}} = {\text{W}}\tan \left( {\varphi - \alpha } \right)$$

D

$${\text{P}} = {\text{W}}\cos \left( {\alpha + \varphi } \right)$$

In a screw jack, the effort required to lift the load is given by (where W = Load lifted, α = Helix angle, and φ = Angle of friction.)

A

P = W tan (α - φ)

B

P = W tan (α + φ)

C

P = W tan (φ - α)

D

P = W cos (α + φ)

In order to ensure self locking in a screw jack, it is essential that helix angle is __________ friction angle.

A

Larger than

B

Smaller than

C

Equal to

D

None of these

While designing a screw in a screw jack against buckling failure, the end conditions for the screw are taken as

A

both ends fixed

B

both ends hinged

C

one end fixed and other end hinged

D

one end fixed and other end free.

The maximum efficiency of spiral gears is (where $$\theta $$ = Shaft angle and $$\varphi $$ = Friction angle)

A

$$\frac{{\sin \left( {\theta + \varphi } \right) + 1}}{{\cos \left( {\theta - \varphi } \right) + 1}}$$

B

$$\frac{{\cos \left( {\theta - \varphi } \right) + 1}}{{\sin \left( {\theta + \varphi } \right) + 1}}$$

C

$$\frac{{\cos \left( {\theta + \varphi } \right) + 1}}{{\cos \left( {\theta - \varphi } \right) + 1}}$$

D

$$\frac{{\cos \left( {\theta - \varphi } \right) + 1}}{{\cos \left( {\theta + \varphi } \right) + 1}}$$

John, Jack, Joseph and Jordan participated in a running race. Only the winner finished the race in 10 minutes. Which two pieces of information can tell you who the winner was? (i) John finished the race in 16 minutes . (ii) Joseph finished the race earlier than Jack by 2 minutes. (iii) Jack finished the race later than Jordan by 4 minutes. (iv) Jordan finished the race earlier than John by 6 minutes. (v) John finished the race later than Joseph by minutes.

A

I and II

B

I and IV

C

II and III

D

II and V

If T is the actual number of teeth on a helical gear and $$\varphi $$ is the helix angle for the teeth, then formative number of teeth is written as

A

$${\text{T}}{\sec ^3}\varphi $$

B

$${\text{T}}{\sec ^2}\varphi $$

C

$$\frac{{\text{T}}}{{{{\sec }^3}\varphi }}$$

D

$${\text{Tcosec}}\varphi $$

The radius of a friction circle for a shaft rotating inside a bearing is (where r = Radius of shaft and $$\tan \varphi $$ = Coefficient of friction between the shaft and bearing)

A

$${\text{r}}\sin \varphi $$

B

$${\text{r}}\cos \varphi $$

C

$${\text{r}}\tan \varphi $$

D

$$\frac{{\text{r}}}{2}\cos \varphi $$

The efficiency of a screw jack is maximum, when (where $$\alpha $$ = Helix angle and $$\varphi $$ = Angle of friction)

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