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  • Stuck here, help me understand: An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1and the second part of mass 2 kg moves with

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1 and the second part of mass 2 kg moves with 8 ms-1 speed. If the third part flies off with 4 ms-1 speed, then its mass is :

  • Option 1)

    17 kg

  • Option 2)

    3 kg

  • Option 3)

    5 kg

  • Option 4)

    7 kg

 

Answers (1)

best_answer

As we learnt in

Law of Consevation of Momentum -

 vec{F}=frac{vec{dp}}{dt}

vec{F}=0            then vec{p}=constant

vec{p}=vec{p}_{1}+vec{p}_{2}+cdots =const

- wherein

ast Independent of frame of reference

 

 

 

p_{1}+p_{2}+p_{3}=0

\therefore 1\times 12\hat{i}+2\times 8\hat{j}+p_{3}=0

p_{3}=-\left \left ( 12\hat{i} \right+16\hat{j} \right )

p_{3}=\sqrt{\left ( 12^\right )^{2}+{(16)^{2}}}

p_{3}=20\ kg-m/s

p_{3}=m_{3}V_{3}

m_{3}=\frac{p_{3}}{V_{3}}=5 kg


Option 1)

17 kg

Incorrect

Option 2)

3 kg

Incorrect

Option 3)

5 kg

Correct

Option 4)

7 kg

Incorrect

Posted by

Aadil

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