Q. 114.2( 164 Votes )

# Two objects, each of mass 1.5 kg, are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 ms^{-1} before the collision during which they stick together. What will be the velocity of the combined objects after collision?

Answer :

Given,

Mass of first object, *m*_{1} = 1.5 kg

Velocity of first object, *v*_{1} = 2.5 m/s

Momentum of first object = m_{1} × v_{1}

= 1.5 × 2.5

= 3.75 kg m/s

Mass of second object, m_{2} = 1.5 kg

Velocity of first object, v_{2} = - 2.5 m/s

So, Momentum of second object, m_{2} × v_{2}

= 1.5 × (-2.5)

= - 3.75 kg m/s

So, Total momentum = 3.75 + (-3.75)

= 0 kg m/s (i)

Combined mass = *m*_{1} + *m*_{2}

= 1.5 + 1.5

= 3.0 kg

Let, the velocity of the combined objects after collision will be v m/s.

Total momentum = (*m*_{1} + *m*_{2}) × *v*

= 3.0 × *v* (ii)

We know that,

According to the principle of conservation of momentum:

Total momentum before collision = Total momentum after collision

0 = 3.0 × *v*

v *=*

*=* 0 m/s

Therefore, the velocity of the combined objects after the collision will be 0 m/s.

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