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Byju's Answer

Standard IX

Physics

Second Law of Motion

Two blocks of...

Question

Two blocks of masses $m_{1}$ and $m_{2}$ , interconnected with a spring of stiffness $K$ , are kept on a smooth horizontal surface. Find out the ratio of velocity, displacement, kinetic energy and acceleration to block with mass $m_{1}$ to block with mass $m_{2}$ .

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Solution

Here $x$ is the displacement, $ν$ is the speed, $p$ is the momentum, $a$ is the acceleration, $K E$ is the kinetic energy, $F$ is the force.
$(F_{e x t})_{s y s t e m} = 0 ⟹ {\to p}_{1} + ⟹ {\to p}_{2} = 0$
$m_{1} ν_{1} = m_{2} ν_{2} ⟹ \frac{ν_{1}}{ν_{2}} = \frac{m_{2}}{m_{1}}$
$m_{1} \int_{0}^{1} ν_{1} d t = m_{2} \int_{0}^{1} ν_{2} d t$
Where $t$ is the time interval of motion of each block.
$m_{1} x_{1} = m_{2} x_{2} ⟹ \frac{x_{1}}{x_{2}} = \frac{m_{2}}{m_{1}}$
$\frac{K E_{1}}{K E_{2}} = \frac{P_{1}^{2} / 2 m_{1}}{P_{2}^{2} / 2 m_{2}} = \frac{m_{2}}{m_{1}}$
$⟹ \frac{F_{1}}{F_{2}} = \frac{k x}{k x}$
Where $x$ is the deformation of the spring.
$∴ \frac{F_{1}}{F_{2}} = 1 ⟹ \frac{m_{1} a_{1}}{m_{2} a_{2}} = 1 ⟹ \frac{a_{1}}{a_{2}} = \frac{m_{2}}{m_{1}}$

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Two blocks of mass m₁ and m₂ interconnected with a spring of stiffness 'k' are kept on a smooth horizontal surface. Which of the following ratios are correct, if the spring was extended and released?

(Where X = displacement, v = speed, P = momentum, a = acceleration, all relative to the surface, KE = kinetic energy, F = force.)

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Two blocks of masses m1 and m2, interconnected with a spring of stiffness K, are kept on a smooth horizontal surface. Find out the ratio of velocity, displacement, kinetic energy and acceleration to block with mass m1 to block with mass m2.

Two blocks of masses $m_{1}$ and $m_{2}$ , interconnected with a spring of stiffness $K$ , are kept on a smooth horizontal surface. Find out the ratio of velocity, displacement, kinetic energy and acceleration to block with mass $m_{1}$ to block with mass $m_{2}$ .