Question

Block A having mass m and block B having mass 3m are held. at rest on a horizontal frictionless surface with a massless spring compressed between them.After the blocks are relaesed from rest,what is the ratio of magnitude of B to Magnitude of A?​

Answer 1

The ratio is 1:3

Explanation:

Given:

Block A and Block B and a spring compressed between them

To find out:

The ratio of the distances traveled by B and A

Solution:

Given

$m_A=m$

$m_B=3m$

Initially the whole system is at rest. After releasing if the velocity of the blocks A and B be $v_A$ and $v_B$ respectively then

As there is no external force acting, the momentum will be conserved

Thus,

Initial momentum = final momentum

$m_A\times 0+m_B\times 0=m_A\times v_A-m_B\times v_B$

$\implies m_Av_A=m_Bv_B$

$\implies m\frac{dx_A}{dt}=3m\frac{dx_B}{dt}$

$\implies x_A=3x_B$

$\implies \frac{x_B}{x_A}=\frac{1}{3}$

$\implies x_B:x_A=1:3$

Hope this answer is helpful.

Know More:

Q: A block of mass 2.0 kg is moving on a frictionless horizontal surface with a velocity of 1.0 m/s (figure 9-E12) towards another block of equal mass kept at rest. The spring constant of the spring fixed at one end is 100 N/m. Find the maximum compression of the spring.

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