Two particles P and Q are moving on circle. At a certain instant of time both the particles are diametrically opposite and P has tangential acceleration 8 m / s 2 and centripetal acceleration 5 m / s

Question

Two particles P and Q are moving on circle. At a certain instant of time both the particles are diametrically opposite and P has tangential acceleration 8 m / s 2 and centripetal acceleration 5 m / s 2 whereas Q has only centripetal acceleration of 1 m / s 2 . At that instant acceleration (in m / s 2 ) of P with respect to Q is

TestHub · Accepted Answer

According to the question, we can draw the following diagram.

From the diagram,

${\vec{a}}_{P} = 5 \hat{i} + 8 \hat{j}$

And ${\vec{a}}_{Q} = - \hat{i}$

Now, ${\vec{a}}_{r e l} = {\vec{a}}_{P} - {\vec{a}}_{Q}$

${\vec{a}}_{r e l} = 5 \hat{i} + \hat{j} - (- \hat{i})$

${\vec{a}}_{r e l} = 6 \hat{i} + 8 \hat{j}$

$|{\vec{a}}_{r e l}| = \sqrt{{(6)}^{2} + {(8)}^{2}} = \sqrt{36 + 64}$

$= \sqrt{100}$

$= 10 m / s^{2}$

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