In the cube of side $'a'$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be:
- $\frac{1}{2} a \left(\hat{i} -\hat{k}\right) $
- $\frac{1}{2} a \left(\hat{j} -\hat{i}\right) $
- $\frac{1}{2} a \left(\hat{k} -\hat{i}\right) $
- $\frac{1}{2} a \left(\hat{j} -\hat{k}\right) $
The Correct Option is B
Solution and Explanation
$ \vec{r}_{H} =\frac{a}{2} \hat{j} + \frac{a}{2} \hat{k} $
$\vec{ r}_{H} - \vec{r}_{g} = \frac{a}{2} \left(\hat{j} - \hat{i}\right) $
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration