Two closely-coiled helical springs 'A' and 'B' are equal in all respects but the number of turns of spring 'A' is double that of spring 'B'. The stiffness of spring 'A' will be __________ that of spring 'B'.

Two closely coiled helical springs 'A' and 'B' are equal in all respects but the diameter of wire of spring 'A' is double that of spring 'B' The stiffness of spring 'B' will be __________ that of spring 'A'

A

One-sixteenth

B

One-eighth

C

One-fourth

D

One-half

Two closely coiled helical springs 'A' and 'B' are equal in all respects but the number of turns of spring 'A' is half that of spring 'B'. The ratio of deflections in spring 'A' to spring 'B' is

A

$$\frac{1}{8}$$

B

$$\frac{1}{4}$$

C

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

D

2

Two helical springs of the same material and of equal circular cross-section, length and number of turns, but having radii 80 mm and 40 mm, kept concentrically (smaller radius spring within the larger radius spring), are compressed between two parallel planes with a load W. The inner spring will carry a load equal to

A

$$\frac{{\text{W}}}{2}$$

B

$$\frac{{2{\text{W}}}}{3}$$

C

$$\frac{{\text{W}}}{9}$$

D

$$\frac{{8{\text{W}}}}{9}$$

Two closely-coiled helical springs 'A' and 'B' of the same material, same number of turns and made from same wire are subjected to an axial load W. The mean diameter of spring 'A' is double the mean diameter of spring 'B'. The ratio of deflections in spring 'B' to spring 'A' will be

A

$$\frac{1}{8}$$

B

$$\frac{1}{4}$$

C

2

D

4

A long helical spring having a spring stiffness of 12 kN/m and number of turns 20, breaks into two parts with number of turns 10 each in both the parts. If the two parts are connected in series, then the softness of the resultant spring will be

A

6 kN/m

B

12 kN/m

C

24 kN/m

D

30 kN/m

Two boysM and N start from the same point. M walks 5 km south, then turns to his left and walks 6 km, then turns to his right and walks 5 km, and then again turns to his right and walks 6 km. At the same time, N walks 5 km north, then turns to his left and walks 6 km, then turns to his left and walks 10 km, and then again turns to his left and walks 3 km and then turns to his right and walks 5 km.What is the position of N with respect to M?

A

6 km to the west

B

3 km to the west

C

8 km to the east

D

4 km to the south

E

10 km to the north

Garima starts walking towards the south from point R. He walks for 5m to reach Point S then turns right and walks for 2m to reach point T from there he turns left and walks for 3m to reach Point Z. He then turns right from point Z and walks for 6m to reach point Y and then turns right and walks for 3m to reach point X. He then turns right from point X and walks for 4m to reach point W and then turns left and walks for 5m to reach point V and then turns left and walks for 4m till point U and stops. What is the shortest distance between point V and point R?

A

4m

B

3m

C

5m

D

8m

An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16MN/m while the stiffness of each rear spring is 32MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

A

6040

B

3020

C

1424

D

955

Two closely coiled helical springs with stiffness k₁ and k₂ respectively are connected in series. The stiffness of an equivalent spring is given by

A

$$\frac{{{{\text{k}}_1}{{\text{k}}_2}}}{{{{\text{k}}_1} + {{\text{k}}_2}}}$$

B

$$\frac{{{{\text{k}}_1} - {{\text{k}}_2}}}{{{{\text{k}}_1} + {{\text{k}}_2}}}$$

C

$$\frac{{{{\text{k}}_1} + {{\text{k}}_2}}}{{{{\text{k}}_1}{{\text{k}}_2}}}$$

D

$$\frac{{{{\text{k}}_1} - {{\text{k}}_2}}}{{{{\text{k}}_1}{{\text{k}}_2}}}$$

An open coiled helical compression spring 'A' of mean diameter 50 mm is subjected to an axial load ‘W’. Another spring 'B' of mean diameter 25 mm is similar to spring 'A' in all respects. The deflection of spring 'B' will be __________ as compared to spring 'A'.

A

One-eighth

B

One-fourth

C

One-half

D

Double

Two closely-coiled helical springs 'A' and 'B' are equal in all respects but the number of turns of spring 'A' is double that of spring 'B'. The stiffness of spring 'A' will be __________ that of spring 'B'.

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