A spring is subjected to two different forces separately. When a force of \(3 ~\text N\) is applied, the spring elongates by \(a\) units, and when a force of \(2 ~\text N\) is applied, the elongation is \(b\) units. What is the value of \((2a – 3b) \text{?}\)
1. \(5\)
2. \(0\)
3. \(7\)
4. \(9\)
Subtopic:  Spring Force |
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Two \(1~\text{kg}\) blocks are connected by a light inextensible string and the system is suspended by a spring of stiffness \(1000~\text{N/m}.\) Take \(g=10~\text{m/s}^2.\)

The extension in the spring, in equilibrium, is:
1. \(1~\text{cm}\) 2. \(2~\text{cm}\)
3. \(0.5~\text{cm}\) 4. \(\sqrt2~\text{cm}\)
Subtopic:  Spring Force |
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A block of mass \(15~\text{kg}\) is suspended using two spring balances of negligible mass, as shown in the figure. Which of the following statements is correct?
      

1. Both scales will read \(15~\text{kg}.\)
2. Both scales will read \(10~\text{kg}.\)
3. The upper scale will read \(15~\text{kg}\) and the lower one zero.
4. The lower scale will read \(15~\text{kg}\) and the upper one zero.
Subtopic:  Spring Force |
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The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration 12 m/sec2. What is the acceleration of 20 kg mass?

(1) 12 m/sec2

(2) 4 m/sec2

(3) 10 m/sec2

(4) Zero

Subtopic:  Spring Force |
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The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration 12 m/sec2. What is the acceleration of 20 kg mass?

1. 12 m/sec2

2. 4 m/sec2

3. 10 m/sec2

4. Zero

Subtopic:  Spring Force |
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When a vertically oriented spring scale supports a \(180\) N block, the spring stretches \(0.3\) m from rest. Neglecting any other masses associated with the scale, what is the value of the spring constant?
1. \(30\) N/m
2. \(294\) N/m
3. \(600\) N/m
4. \(5880\) N/m
Subtopic:  Spring Force |
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A block (mass: \(m\)) is being pulled horizontally on a rough horizontal surface \(\left(\mu=\dfrac12\right)\) by means of a spring of spring constant \(k.\) The maximum extension in the spring before the block moves is:
1. \(\dfrac{mg}{k}\) 2. \(\dfrac{mg}{2k}\)
3. \(\dfrac{2mg}{k}\) 4. \(\dfrac{3mg}{2k}\)
Subtopic:  Spring Force |
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A spring of force constant k is cut into lengths of ratio 1:2:3. They are connected in series and the new force constant is k'. If they are connected in parallel and force constant is k'',thenk':k'' is 

(1) 1:6

(2) 1:9

(3) 1:11

(4) 6:11

Subtopic:  Spring Force |
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