Ratio of work done in stretching springs with different constants – Rankers Physics

Potential Energy & Equilibrium: Practice Problem & Solution

Two springs \(A\) and \(B\) (\(K_A = 2K_B\)) are stretched by same suspended weights then ratio of work done in stretching is (1999)
\(1:2\)
\(2:1\)
\(1:1\)
\(1:4\)

Solution Explained:

To solve this problem, we apply the core principles of Potential Energy & Equilibrium. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Work done to stretch a spring under a constant force. Formula: \(W = \frac{F^2}{2K}\). When the same force \(F\) (due to suspended weights) is applied, the work done is inversely proportional to the spring constant (\(W \propto 1/K\)). Given \(K_A = 2K_B\). The ratio of work done is \(\frac{W_A}{W_B} = \frac{1/K_A}{1/K_B} = \frac{K_B}{K_A}\). Substituting \(K_A = 2K_B\), we get \(\frac{W_A}{W_B} = \frac{K_B}{2K_B} = \frac{1}{2}\). So the ratio is \(1:2\).

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A particle of mass 4 kg is performing S.H.M. in a straight line under the action of force \( F = (15 - 3x) \text{ N} \). Equilibrium position of particle will be
2. The only force acting on a \(2\text{ kg}\) body as it moves along the positive x axis has component \(F_x = -6x\text{ N}\), where x is in metre. The velocity of the body at \(x = 3\text{ m}\) is \(8\text{ m/s}\). The velocity of the body at \(x = 4\text{ m}\) is:
3. Assertion (A): There is no term like instantaneous work similar to instantaneous velocity. Reason (R): For work to be done, the force must act for a displacement.  
4. A vertical spring with force constant \(k\) is fixed on a table. A ball of mass \(m\) at a height \(h\) above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance \(d\). The net work done in the process is: (2007)
5. Assertion (A): The kinetic energy of a particle continuously increases with time if the resultant force on the particle must be at an angle less than \(90^{\circ}\) to the velocity at all instants. Reason (R): The work done by the external forces on a system equals to change in total energy.