Question

A 2500kg wagon moving at 2 m/s collides with 5000kg wagon at rest. They couple upon collision and move away atRequired to answer. Single choice.



2 m/s

2/3 m/s

1 m/s

1/3 m/s

​

Answer 1

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★ Question :

A 2500 kg wagon moving at 2 m/s collides with 5000 kg wagon at rest. They couple upon collision and move away at

1. 2 m/s
2. 2/3 m/s
3. 1 m/s
4. 1/3 m/s

★ Solution :

Mass of the 1st wagon (m) = 2500 kg

Initial Velocity of the 1st wagon (u) = 2 m/s

Mass of the 2nd wagon (M) = 5000 kg

Initial Velocity of the 2nd wagon (U) = 0 m/s

[ ∵ 5000 kg wagon is at rest  ]

Now they couple are in collision and moving with some velocity .

Mass of the couple , (m + M)

                                 = 2500 + 5000

                                 = 7500 kg        

Velocity of the couple (V) = ? m/s

Apply Conservation of momentum ,

$:\implies \sf \orange{P_{Initial}=P_{Final}}$

$:\implies \sf mu+MU=(m+M)V$

$:\implies \sf (2500)(2)+(5000)(0)=(7500)V$

$:\implies \sf 5000=7500V$

$:\implies \sf V=\dfrac{5000}{7500}$

$:\implies \sf \pink{V=\dfrac{2}{3}\ m/s}\ \; \bigstar$

Velocity of the couple is 2/3 m/s .

Option (2)

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Answer 2

$\Large{\bf{\green{\underline{GiVeN,\::}}}}$

• m₁ = 2500 kg

• u₁ = 2 m/s

• m₂ = 5000 kg

• u₂ = 0 m/s (at rest)

$\\ \Large{\bf{\pink{\underline{To\:FiNd,\::}}}}$

• The velocity at which couple collides.

$\\ \Large{\purple{\underline{\textsf{\textbf{Step-by-step\:Explanation\::}}}}}$

We know that,

➣ The magnitude of the linear momentum of a body is the product of the mass of the body and the speed of the body.

➻ First we calculate the initial momentum. To calculate initial momentum, we follow the following steps,

$\longmapsto\:\:\bf{P_{(initial)}\:=\:m_1\:u_1\:+\:m_2\:u_2\:}$

$\longmapsto\:\:\bf{P_{(initial)}\:=\:2500\times{2}\:+\:5000\times{0}\:}$

$\longmapsto\:\:\bf{P_{(initial)}\:=\:5000\:+\:0\:}$

$\longmapsto\:\:\bf{P_{(initial)}\:=\:5000\:kg.m/s}--(1)$

$\Large\bf\pink{Let,}$

↝ After collision, the two cars move at the same speed, i.e. v. Thus,

$\longmapsto\:\:\bf{Final\:momentum\:\Big(P_{(final)}\Big)\:=\:(m_1\:+\:m_2)\:v\:}$

$\longmapsto\:\:\bf{P_{(final)}\:=\:(2500\:+\:5000)\times{v}\:}$

$\longmapsto\:\:\bf{P_{(final)}\:=\:(7500\:v)\:kg.m/s}--(2)$

$\bf\orange{Acc.\:to\:Conservation\:of\:Linear\:Momentum,}$

➻ The total linear momentum of the two freight cars before collision must be equal to the total linear momentum after the collision.

$\\ \red\checkmark\:\:\bf\green{P_{(initial)}\:=\:P_{(final)}\:}$

$:\implies\:\:\bf{5000\:=\:7500\:v\:}$

$:\implies\:\:\bf{v\:=\:\dfrac{5000}{7500}}$

$:\implies\:\:\bf\purple{v\:=\:\dfrac{2}{3}\:m/s}$

━─━─━─━─━─━─━─━─━─━─━─━─━─━─━

$\Large\bf\blue{Therefore,}$

2) The velocity, at which couple collides, is $\bf{\dfrac{2}{3}\:m/s}$.