A force on an object of mass 100, g is (10 ha | vedclass

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(A) Given: Force $\vec{F} = (10 \hat{i} + 5 \hat{j})\ N$,mass $m = 100\, g = 0.1\, kg$,initial velocity $\vec{u} = 0$,time $t = 2\ s$.Using Newton's s

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(A) Given: Force $\vec{F} = (10 \hat{i} + 5 \hat{j})\ N$,mass $m = 100\, g = 0.1\, kg$,initial velocity $\vec{u} = 0$,time $t = 2\ s$.Using Newton's second law,acceleration $\vec{a} = \frac{\vec{F}}{m} = \frac{10 \hat{i} + 5 \hat{j}}{0.1} = (100 \hat{i} + 50 \hat{j})\ m/s^2$.Using the equation of motion $\vec{s} = \vec{u}t + \frac{1}{2} \vec{a} t^2$,since $\vec{u} = 0$:$\vec{s} = \frac{1}{2} (100 \hat{i} + 50 \hat{j}) (2)^2$$\vec{s} = \frac{1}{2} (100 \hat{i} + 50 \hat{j}) (4) = 2 (100 \hat{i} + 50 \hat{j}) = (200 \hat{i} + 100 \hat{j})\ m$.Comparing this with $(a \hat{i} + b \hat{j})\ m$,we get $a = 200$ and $b = 100$.Therefore,$\frac{a}{b} = \frac{200}{100} = 2$.

$A$ force on an object of mass $100\, g$ is $(10 \hat{i}+5 \hat{j})\ N$. The position of that object at $t= 2\ s$ is $(a \hat{i}+b \hat{j})\, m$ after starting from rest. The value of $\frac{a}{b}$ will be..........

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