A particle of mass 1-0 g moving with velocity v-1-3-0i-2-0j- experiences a perfectly inelastic collision with another particle of mass 2-0 g and velocity v-2-4-0j-6-0k- If the velocity of the formed particle is 40-x10 m-s- if the components of the vectors v-1- and v-2- are given in the SI units- Find x-

From conservation of momentum, for the closed system #34;both colliding particles #34; m_1v⃗_⃗1⃗+m_2v⃗_⃗2⃗=(m_1+m_2)v⃗ or, v⃗=m_1v⃗_⃗1⃗+m_2v⃗_⃗2⃗m ...

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

Byju's Answer

Standard XII

Physics

Velocity of COM

A particle of...

Question

A particle of mass $1.0 g$ moving with velocity $_{1} = 3.0 \to i - 2.0 \to j$ experiences a perfectly inelastic collision with another particle of mass $2.0 g$ and velocity $_{2} = 4.0 \to j - 6.0 \to k$ . If the velocity of the formed particle is $\frac{40 + x}{10} m / s$ , if the components of the vectors $_{1}$ and $_{2}$ are given in the SI units. Find $x$ :

Open in App

Solution

From conservation of momentum, for the closed system "both colliding particles"

$m_{1}_{1} + m_{2}_{2} = (m_{1} + m_{2}) \to v$

or, $\to v = \frac{m_{1}_{1} + m_{2}_{2}}{m_{1} + m_{2}} = \frac{1 (3 \to i - 2 \to j) + 2 (4 \to j - 6 \to k)}{3} = \to i + 2 \to j - 4 \to k$

Hence $| \to v | = \sqrt{1 + 4 + 16} m / s = 4.6 m / s$

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. Two particles of masses

m_{1}

and

m_{2}

are moving velocities

_{1}

and

_{2}

Momentum of the particle of mass

m_{1}

with respect to center of mass is

Q. Velocity of a particle of mass 2 kg changes from

_{1} = - 2 ˆ i - 2 ˆ j m / s

_{2} = (ˆ i - ˆ j) m / s

after colliding with a plane surface

Q. Find the increment of the kinetic energy of the closed system comprising two spheres of masses

m_{1}

and

m_{2}

due to their perfectly inelastic collision, if the initial velocities of the spheres were equal to

_{1}

and

_{2}

Join BYJU'S Learning Program

From conservation of momentum, for the closed system "both colliding particles"m1→v1+m2→v2=(m1+m2)→vor, →v=m1→v1+m2→v2m1+m2=1(3→i−2→j)+2(4→j−6→k)3=→i+2→j−4→kHence |→v|=√1+4+16m/s=4.6m/s