Springs in Series and Parallel

Q. If two springs of stiffness $k_{1}and{k}_2$ are connnected in series, the stiffness of the combined spring is

1. $\frac{k_1{k}_2}{k_1+k_2}$
2. $\frac{k_1+k_2}{k_1{k}_2}$
3. $k_1+k_2$
4. $k_1{k}_2$

Q.

Does diameter affect spring constant

Q. What is the equivalent spring stiffness for the system of springs shown in the figure given below?

1. 43 kN/m
2. 50 kN/m
3. 58 kN/m
4. 64 kN/m

Q. If three close-coiled and two open-coiled helical springs, each having the stiffness 'k' are connected in series than the overall stiffness is

1. 5k
2. k/5
3. $k/\sqrt{5}$
4. 6k/5

Q. If the wire diameter of a compressive helical spring is increased by 2 %, the change in spring stiffness(in %) is _____ ( correct to two decimal places)

1. 8.243

Q. A compression spring is made of music wire of 2mm diameter having a shear strength and shear modulus of 800 MPa and 80 GPa respectively. The mean coil diameter is 20 mm, free length is 40 mm and the number of active coils is 10. If the mean coil diameter is reduced to 10 mm, the stiffness of the spring is approximately

1. decreased by 8 times
2. decreased by 2 times
3. increased by 2 times
4. increased by 8 times

Q. A helical spring has constant k. If the wire diameter, spring diameter and the number of coils are all doubled, then, the spring constant of the new spring becomes

1. 8k
2. 16k
3. k
4. k/2

Q. Two co-axial springs are subjected to a force of 1 kN. Spring constant of larger diameter spring is 80 N/mm and that of smaller diameter spring is 120 N/mm. The deformation in the spring combination will be equal to

1. 5 mm
2. 15 mm
3. $\frac{125}{6}mm$
4. $\frac{135}{7}mm$

Q. The spring constant of a helical compression spring DOES NOT depend on

1. Coil diameter
2. material strength
3. number of active turns
4. wire diameter

Q. The figure shows arrangements of springs. They have stiffness $k_1$ and $k_2$ as marked. Which of the following arrangements offers a stifness = $\frac{2k_1{k}_2}{k_1+2k_2}?$

1. 
2. 
3. 
4. 

Q. Two closed coil springs of stiffness k and 2k are arranged in series in one case and in parallel in the other case. The ratio of stiffness of springs connected in series to parallel is

1. $\frac{1}{3}$
2. $\frac{1}{9}$
3. $\frac{2}{3}$
4. $\frac{2}{9}$

Q. The close-coiled spring shown in Fig-I is cut into two equal pieces which are combined to form a parallel spring as shown in Fig-II. The ratio of the angular twist for the spring is Fig-II to that of spring in Fig-I due to an axial load P is

1. 1/2
2. 1/4
3. 1/8
4. 1