Question

Consider the situation shown in figure. Mass of the block and the pulley is m. Assume that string and spring are light, find the elongation of the spring at equilibrium.





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Answer 1

The answer is Option a) 2mg/k

Answer 2

Given:

A system with a light spring, attached to an ideal pulley and a mass m

To Find:

The elongation of the spring at equilibrium

Solution:

At equilibrium position, the net upward force on the mass m will equal the net downward force on it.

The upward force acting on the block is the tension in the string (T) and the downward force is mg.

⇒ T = mg

The spring when pulled downwards produces an equal and opposite restoring force.

Spring Force = k.x  

(k = spring constant; x= elongation in the spring)

Since the net downward force = 2 X T

⇒ k.x = 2 XT

or x = 2T/k

Since T=mg,

x = 2mg/k

Hence, the elongation in the spring at equilibrium position is 2mg/k meter.