In a wheel and differential axle, the diameter of the effort wheel is 400 mm. The radii of the load axles are 150mm and 100 mm respectively. The diameter of the rope is 10 mm. Find the load which can be lifted by an effort of 100 N, assuming an efficiency of the machine to be 75%.

The velocity ratio of a differential wheel and axle with 'D' as the diameter of effort wheel and d₁ and d₂ as the diameters of larger and smaller axles respectively, is

A

$$\frac{{\text{D}}}{{{{\text{d}}_1} + {{\text{d}}_2}}}$$

B

$$\frac{{\text{D}}}{{{{\text{d}}_1} - {{\text{d}}_2}}}$$

C

$$\frac{{2{\text{D}}}}{{{{\text{d}}_1} + {{\text{d}}_2}}}$$

D

$$\frac{{2{\text{D}}}}{{{{\text{d}}_1} - {{\text{d}}_2}}}$$

In a weston differential pulley block, the number of recesses in the smaller wheel is 9/10 of that of the larger wheel. If the efficiency of the machine is 50%, find the load lifted by an effort of 300N.

A

2000N

B

3000N

C

4000N

D

none of the mentioned

The velocity ratio of a simple wheel and axle with D and d as the diameters of effort wheel and load axle, is

A

D + d

B

D - d

C

D × d

D

$$\frac{{\text{D}}}{{\text{d}}}$$

A lift of weight W is lifted by a rope with an acceleration f. If the area of cross-section of the rope is A, the stress in the rope is

A

$$\frac{{{\text{W}}\left( {1 + \frac{{\text{f}}}{{\text{g}}}} \right)}}{{\text{A}}}$$

B

$$\frac{{\left( {1 - \frac{{\text{g}}}{{\text{f}}}} \right)}}{{\text{A}}}$$

C

$$\frac{{{\text{W}}\left( {2 + \frac{{\text{f}}}{{\text{g}}}} \right)}}{{\text{A}}}$$

D

$$\frac{{{\text{W}}\left( {2 + \frac{{\text{g}}}{{\text{f}}}} \right)}}{{\text{A}}}$$

A man ordered a length of rope by telephone from his nearest hardware shop. But when a worker in the shop brought the rope, he found that the man on the telephone had miswritten the order by interchange feet and inches. As a result of this, the length of rope received was only 30% of the length he had ordered. The length of the rope which the man ordered was between :

A

6 ft and 7 inches

B

7$$\frac{1}{2}$$ ft and 9 ft

C

9 ft and 2 inches

D

10$$\frac{1}{2}$$ ft and 12 ft

Two persons are holding a rope of negligible mass horizontally. A 20 kg mass is attached to the rope at the mid-point, as a result, the rope deviates from the horizontal direction. The tension required to completely straighten the rope is (g = 10 m/s²)

A

200 N

B

20 N

C

10 N

D

infinitely large

An elevator is assembled to raise equipment to a height of 22m. It is estimated that maximum weight of the material to be raised is 4.9kN. It is observed acceleration in such cases is 1.2m/s².10mm diameter wire ropes with fibre core are used. The tensile designation of the wire is 1500.Number of rope wires is assumed to be 2. Number of rope wires is assumed to be 2. Calculate the total load on wire rope neglecting the bending load if weight of 50m wire is 18kg.

A

1054.55N

B

3504.55N

C

2836.84N

D

5678.6N

The fundamental equation for correct steering is (where $$\varphi $$ and $$\alpha $$ = Angle through which the axis of the outer wheel and inner wheel turns respectively, c = Distance between the pivots of the front axles and d = Wheel base)

A

$$\sin \varphi + \sin \alpha = \frac{{\text{b}}}{{\text{c}}}$$

B

$$\cos \varphi - \sin \alpha = \frac{{\text{c}}}{{\text{b}}}$$

C

$$\cot \varphi - \cot \alpha = \frac{{\text{c}}}{{\text{b}}}$$

D

$$\tan \varphi + \cot \alpha = \frac{{\text{b}}}{{\text{c}}}$$

A machine vice whose length of the handle is 150mm and the coefficient of friction for thread and collar are 0.15 and 0.17 respectively has a force applied at handle of 125N. Also the outer and inner diameters of collar are 55mm and 45mm respectively. Find the collar torque in terms of clamping force W assuming uniform wear theory if nominal diameter=22mm and pitch=5mm.

A

4.5W

B

5.4W

C

4.25W

D

3.37W

A direct rope haulage pulls 8 tubs loaded with coal through an incline of length 500 m having an inclination of 1 in 6. Consider the following additional data.
Capacity of tub = 1.0 tonne.
Tare weight of tub = 500 kg
Hauling speed = 9 km per hour
Coefficient of friction between wheel and rail = $$\frac{1}{{60}}$$
Coefficient of friction between rope and drum = $$\frac{1}{{10}}$$
Mass of rope per meter = 1.5 kg
The minimum power required to haul the tubs in kW is

A

345.50

B

348.60

C

350.10

D

365.50

E

58.86

In a wheel and differential axle, the diameter of the effort wheel is 400 mm. The radii of the load axles are 150mm and 100 mm respectively. The diameter of the rope is 10 mm. Find the load which can be lifted by an effort of 100 N, assuming an efficiency of the machine to be 75%.

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