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Standard XII

Physics

Constrained Motion : Intuitive Approach

A block of ma...

Question

A block of mass $m$ is connected to a massless pulley and massless spring of stiffness $k .$ The pulley is frictionless, and the string is massless. Initially, the block is not hanging, it is supported by some unknown support. Also, the spring is not stretched when the block is released. When the block is released, the spring is maximum stretched. Find the ratio of tension in the rope and weight of the block (give integer value)

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Solution

Let the maximum stretched in the spring is $x$ .

Using conservation of mechanical energy,

$m g x = \frac{1}{2} k x^{2}$

$∴ k x = 2 m g$

Tension in the string, $T = k x$

$\Rightarrow T = 2 m g$

Weight of the block, $W = m g$

$∴ \frac{T}{W} = \frac{2 m g}{m g} = 2$

Correct answer $: 2$

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Constrained Motion : Intuitive Approach

Standard XII Physics

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Let the maximum stretched in the spring is x. Using conservation of mechanical energy, mgx=12kx2 ∴kx=2mg Tension in the string, T=kx ⇒T=2mg Weight of the block, W=mg ∴TW=2mgmg=2 Correct answer:2

Let the maximum stretched in the spring is $x$ .

Using conservation of mechanical energy,

$m g x = \frac{1}{2} k x^{2}$

$∴ k x = 2 m g$

Tension in the string, $T = k x$

$\Rightarrow T = 2 m g$

Weight of the block, $W = m g$

$∴ \frac{T}{W} = \frac{2 m g}{m g} = 2$

Correct answer $: 2$