You visited us 1 times! Enjoying our articles? Unlock Full Access!

Examples

A spring is c...

Question

A spring is compressed between two blocks of masses $m_{1}$ and $m_{2}$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $v_{1}$ and $v_{2}$ as shown. The blocks travel distances $x_{1}$ and $x_{2}$ respectively before coming to rest.
The ratio $(\frac{x_{1}}{x_{2}})$ is

\frac{m_{2}}{m_{1}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{m_{1}}{m_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{\frac{m_{2}}{m_{1}}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{\frac{m_{1}}{m_{2}}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{m_{2}}{m_{1}}$
Initial momentum of the system is zero, i.e.

$P_{i} = 0$

Given, the velocity acquire by masses $m_{1}$ and $m_{2}$ just after they are released be $v_{1}$ and $v_{2}$ .

Final momentum of the system,

$P_{f} = m_{2} v_{2} - m_{1} v_{1}$

Using conservation of momentum,

$P_{i} = P_{f}$

$∴ 0 = m_{2} v_{2} - m_{1} v_{1}$

$\Rightarrow m_{2} x_{2} - m_{1} x_{1} = 0 [∵ v = \frac{d x}{d t}]$

$\Rightarrow \frac{x_{1}}{x_{2}} = \frac{m_{2}}{m_{1}}$

Hence, $(A)$ is the correct answer.

Suggest Corrections

Similar questions

Q. A spring is compressed between two blocks of masses

m_{1}

and

m_{2}

placed on a horizontal frictionless surface. When the blocks are released, the blocks travel distance

x_{1}

and

x_{2}

respectively before coming to rest. The ratio

x_{1} / x_{2}

is:

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.)

Q. Two blocks of masses

m_{1} = 1 k g

and

m_{2} = 2 k g

are connected by massless strings and placed on a horizontal frictionless surface as shown in figure. A force

F = 12 N

is applied to mass

m_{1}

as shown then tension

(T)

between

m_{1}

and

m_{2}

Q. Two blocks

M_{1}

and

M_{2}

having equal masses are to move on a horizontal frictionless surface.

M_{2}

is attached to a massless spring as shown in figure. Initially,

M_{2}

is at rest and

M_{1}

is moving toward

M_{2}

with speed

v

and collides head-on with

M_{2}

Q. Two blocks

m_{1}

and

m_{2}

are placed on a smooth horizontal surface; and are joined together with a spring of stiffness

k

as shown in the figure. Suddenly, the block

m_{2}

receives a horizontal velocity

v_{0}

Join BYJU'S Learning Program