A body of mass 'm' moving with speed $3 \mathrm{~m} / \mathrm{s}$ collides with a body of mass ${ }^{4} 2…

A body of mass 'm' moving with speed $3 \mathrm{~m} / \mathrm{s}$ collides with a body of mass ${ }^{4} 2 \mathrm{~m}^{\prime}$ at rest. The coalesced mass will start to move with a speed of
  1. $3 \mathrm{~m} / \mathrm{s}$
  2. $6 \mathrm{~m} / \mathrm{s}$
  3. $9 \mathrm{~m} / \mathrm{s}$
  4. $1 \mathrm{~m} / \mathrm{s}$

Solution

Initial velocity of moving mass $\mathrm{u}_{1}=3 \mathrm{~km} / \mathrm{h}$ Initial velocity of stationary mass $\mathrm{u}_{2}=0$ Thus momentum of the system initially $P_{i}=m_{1} u_{1}+m_{2} u_{2}$ $\therefore P_{i}=3 m+0=3 m$ Let the velocity of coalesced mass be V. Thus momentum of the system finally $\mathrm{P}_{\mathrm{f}}=\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{V}=3 \mathrm{mV}$ Using conservation of linear momentum $P_{i}=P_{f}$ $\therefore 3 \mathrm{~m}=3 \mathrm{~mV}$ $\Rightarrow \mathrm{V}=1 \mathrm{~m} / \mathrm{h}$ .

Asked in: MHT CET 2020 (20 Oct Shift 2)

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