If a force 10 hat{i} + 15 hat{j} + 25 hat{k} | vedclass

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(D) According to Newton's second law for a system of particles,the external force acting on the system is related to the acceleration of the centre of

Vedclass · Accepted Answer

given data is not correct

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(D) According to Newton's second law for a system of particles,the external force acting on the system is related to the acceleration of the centre of mass by the equation: $\vec{F}_{ext} = M \vec{a}_{CM}$.This implies that the acceleration vector $\vec{a}_{CM}$ must be in the same direction as the external force vector $\vec{F}_{ext}$.Given $\vec{F}_{ext} = 10 \hat{i} + 15 \hat{j} + 25 \hat{k} = 5(2 \hat{i} + 3 \hat{j} + 5 \hat{k})$.Given $\vec{a}_{CM} = 2 \hat{i} + 3 \hat{j} - 5 \hat{k}$.Comparing the components,we see that the $z$-component of the force is positive $(+25 \hat{k})$,while the $z$-component of the acceleration is negative $(-5 \hat{k})$.Since the vectors are not parallel,the given data is physically inconsistent. Therefore,the correct option is $D$.

If a force $10 \hat{i} + 15 \hat{j} + 25 \hat{k}$ acts on a system and gives an acceleration $2 \hat{i} + 3 \hat{j} - 5 \hat{k}$ to the centre of mass of the system,the mass of the system is

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