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A body under the action of a force \vec{F}=6\hat{i}-8\hat{j}+10\hat{k}, acquires an acceleration of 1m/s2. The mass of this body must be 

  • Option 1)

    10kg

  • Option 2)

    20kg

  • Option 3)

    10\sqrt{2}kg

  • Option 4)

    2\sqrt{10}kg

 

Answers (1)

best_answer

As we discussed in concept

Newton's 2nd Law -

F\propto \frac{dp}{dt}

F=\tfrac{kdp}{dt} 

F=\tfrac{d\left (mv \right )}{dt} 

F=\tfrac{m\left (dv \right )}{dt}

\frac{dv}{dt}=a

Therefore  F=ma

- wherein

K=1 in C.G.S & S.I

 

 \vec{F}=6\hat{i}-8\hat{j}+10\vec{K}                                  = \left | \vec{F} \right |\:=\:\sqrt{36+64+100}=\sqrt{200}N

\left | \vec{F} \right | = 10 \sqrt{2}N

Given \vec{a}=1\:m/s^{2}

\mu\:=\: \frac{10\sqrt{2}}{1}=10\sqrt{2}kg


Option 1)

10kg

This option is incorrect.

Option 2)

20kg

This option is incorrect.

Option 3)

10\sqrt{2}kg

This option is correct.

Option 4)

2\sqrt{10}kg

This option is incorrect.

Posted by

Aadil

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