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

The 'e' Equation

A particle of...

Question

A particle of mass $m_{1} = 4$ kg moving at 6 $ˆ i$ ms $^{- 1}$ collides perfectly elastically with a particle of mass $m_{2} = 2 k g$ moving at 3 $ˆ i$ ms $^{- 1}$

velocity of centre of mass (CM) is 5

ˆ i

^{- 1}

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

the velocities of the particle relative to the centre of mass have same magnitude.

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

speed of individual particle before and after collision remains same.

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

the velocity of particle relative to CM after collision are

{\to v}_{1 f / c m} = - ˆ i m s^{- 1}, {\to v}_{2 f / c m} = 2 ˆ i m s^{- 1}

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

Open in App

Solution

The correct options are
A velocity of centre of mass (CM) is 5 $ˆ i$ ms $^{- 1}$
D the velocity of particle relative to CM after collision are ${\to v}_{1 f / c m} = - ˆ i m s^{- 1}, {\to v}_{2 f / c m} = 2 ˆ i m s^{- 1}$
$V_{c o m} = \frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}} = \frac{4 \times 6^i + 2 \times 3^i}{4 + 2} = 5^i {\to v}_{1 i n / c o m} = {\to v}_{1} - {\to v}_{c o m} = 6^i - 5^i =^i {\to v}_{2 i n / c o m} = {\to v}_{2} - {\to v}_{c o m} = 3^i - 5^i = - 2^i$

From the frame of COM the velocities in elastic collision are just reversed.
So, ${\to v}_{1 f / c o m} = {\to v}_{1} - {\to v}_{c o m} = 6^i - 5^i =^i {\to v}_{2 f / c o m} = {\to v}_{2} - {\to v}_{c o m} = 3^i - 5^i = - 2^i$

Suggest Corrections

Similar questions

Q. A particle of mass

1 g

moving with a velocity

_{1} = 3^i - 2^j m s^{- 1}

experiences a perfectly in elastic collision with another particle of mass

2 g

and velocity

_{2} = 4^j - 6^k m s^{- 1}

. The velocity of the particle is:

Q. A particle of mass

1

g moving with a velocity

_{2} = (3^i - 2^j)

m s^{- 1}

experiences a perfectly inelastic collision with another particle of mass

2

g and velocity

_{2} = (4^j - 6^k) m s^{- 1}

. The velocity of the combined particle is?

Q. A particle of mass

m

moving with a velocity

(3^i + 2^j) m s^{- 1}

collides with another body of

mass

M

and finally moves with velocity

(- 2^i +^j) m s^{- 1}

. Then during the collision :

Q. Particle

A

of mass

m_{1}

moving with velocity

(\sqrt{3}^i +^j) m s^{- 1}

collides with another partice

B

of mass

m_{2}

which is at rest initially. Let

_{1}

and

_{2}

be the velocities of particles

A

and

B

after collision respectively. If

m_{1} = 2 m_{2}

and after collision

_{1} = (^i + \sqrt{3}^j) m s^{- 1},

the angle between

_{1}

and

_{2}

is :

Q. Two perfectly elastic particles A and B of equal masses travelling along the line joining them with velocity 15 ms

^{- 1}

and 10 ms

^{- 1}

respectively collide. Their velocities after the elastic collision will be (in ms

^{- 1}

) respectively :

Join BYJU'S Learning Program

A particle of mass m1=4 kg moving at 6ˆi ms−1 collides perfectly elastically with a particle of mass m2=2kg moving at 3ˆi ms−1

A particle of mass $m_{1} = 4$ kg moving at 6 $ˆ i$ ms $^{- 1}$ collides perfectly elastically with a particle of mass $m_{2} = 2 k g$ moving at 3 $ˆ i$ ms $^{- 1}$