MyQuestionIcon

1

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

Final Velocities

A moving body...

Question

A moving body with a mass $m_{1}$ and velocity u strikes a stationary body of mass $m_{2}$ . The masses $m_{1}$ and $m_{2}$ should be in the ratio $m_{1} / m_{2}$ so as to decrease the velocity of the first body to $2 u / 3$ and giving a velocity of $v$ to $m_{2}$ assuming a perfectly elastic impact. Then the ratio $m_{1} / m_{2}$ is :

A

5

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

B

1 / 5

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

C

1 / 25

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

D

25

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

Open in App

Solution

The correct option is A $5$
$m_{1} u = m_{1} \frac{2 u}{3} + m_{2} v$ (By conservation of linear momentum)
$\Rightarrow \frac{1}{3} m_{1} u = m_{2} v$ .................(i)
Also $e = \frac{| v_{1} - v_{2} |}{| u_{2} - u_{1} |}$
$\Rightarrow v - \frac{2 u}{3} = u \Rightarrow v = \frac{5}{3} u$ ............(ii)
From (i) and (ii), $\frac{1}{3} m_{1} u = \frac{5}{3} m_{2} u \Rightarrow \frac{m_{1}}{m_{2}} = 5$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A moving body with a mass

m_{1}

strikes a stationary body of mass

m_{2}

m_{1}

m_{2}

should be in the ratio so as to decrease the velocity of the first body 1.5 times, assuming a perfectly elastic impact. Then, the ratio

m_{1} : m_{2}

Q. A moving body of mass

m_{1}

strikes a stationary body of mass

m_{2}

m_{1}

m_{2}

should be in the ratio

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

so as to decrease the velocity of the first body 1.5 times assuming a perfectly elastic impact. Then the ratio

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

Q. A body of mass

m_{1}

moving with an unknown velocity of

v_{1}^i

, undergoes a collinear collision with a body of mass

m_{2}

moving with a velocity

v_{2}^i

. After collision,

m_{1}

m_{2}

move with velocities of

v_{3}^i

v_{4}^i

, respectively.
If

m_{2} = 0.5 m_{1}

v_{3} = 0.5 v_{1}

v_{1}

Q. When a body of mass

m_{1}

moving with uniform velocity

40 m s^{- 1}

collides with another body of mass

m_{2}

at rest, then the two together begin to move with uniform velocity of

30 m s^{- 1}

. The ratio of the mass (i.e.,

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

) of the two bodies will be

Q. Two balls of masses

m_{1} and m_{2}

m_{2} >> m_{1}

) are moving with initial velocities

v_{1} and v_{2}

respectively towards each other. The final velocity of

m_{2}

after collision will be [Assume collision to be perfectly elastic]

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

A No-Loss Collision

PHYSICS

Watch in App

explore_more_icon

Explore more

Final Velocities

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon