Closely Coiled Helical Springs

Q. A close-coiled helical spring with n coils, mean radius R and diameter 'd' is subjected to an axial load W. What is the compression in spring?

1. $\frac{64W{R}^{3}n}{C{d}^3}$
2. $\frac{64W{R}^{3}n}{C{d}^4}$
3. $\frac{32W{R}^{3}n}{C{d}^3}$
4. $\frac{32W{R}^{3}n}{C{d}^4}$

Q. A closely coiled helical spring of round steel wire 5 mm in diameter having 12 complete coils of 50 mm mean diameter is subjected to an axial load of 100 N. Modulus of Rigidity of the spring is $80kN/m{m}^2$. What is the deflection of the spring?

1. 12 mm
2. 24 mm
3. 36 mm
4. 48 mm

Q. A uniform T-shaped arm of weight W, pinned about a horizontal point $C$, is supported by a vertical spring of stiffness $K$, The extension of the spring is

1. $\frac{3W}{4K}$
2. $\frac{4W}{3K}$
3. $\frac{3K}{4W}$
4. $\frac{4K}{3W}$

Q. Two closely coiled helical springs A and B are respects but for the number of turns, with A having just half the number of turns of that B. What is the ratio of deflections in terms of spring A to spring B?

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

Q. A close-coiled helical spring shown below in Fig-I is to be cut into two equal pieces and combined as a parallel spring as shown in Fig-II. The ratio shown in Fig-II to that of Fig-I, due to the same load W will be

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

Q. A close helical spring of 100 mm mean diameter is made of 10 mm diameter rod, and has 20 turns. The springs carries an axial load of 200 kN with $G=8.4\times {10}^{4}N/m{m}^2$. The stiffness of the spring is nearly

1. 5.25 N/mm
2. 6.50 N/mm
3. 7.25 N/mm
4. 8.50 N/mm

Q. The equivalent spring constant for the set up shown in the below figure, where EI = unity throughout is

1. 30 units
2. 36 units
3. 40 units
4. 48 units