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A particle is moving with speed $v = 2 t^{2}$ on the circumference of circle of radius $R$ . Match the quantities given in Column-I with corresponding results in Column-II.
Column 1 Column 2
A) Magnitude of tangential acceleration of particle P) decreases with time
B) Magnitude of centripetal acceleration of particle Q) increases with time
C) Magnitude of angular speed of particle with respect to centre of circle R) remains constant
D) Value of tan $θ$ , where $θ$ is angle between the total acceleration vector and centripetal acceleration vector of particle S) proportional to R
T) Inversely proportional to R

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$A \to Q; B \to Q, T; C \to Q, T; D \to P, S$

$A \to Q; B \to Q, T; C \to Q, T; D \to P, T$

$A \to Q, T; B \to Q, T; C \to Q, T; D \to P$

$A \to Q, R; B \to Q, T; C \to Q, T; D \to P$

answer is B.

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Detailed Solution

$v = 2 t^{2}$

Tangential acceleration $a_{t} = 4 t$

Centripetal acceleration $a_{c} = \frac{v^{2}}{R} = \frac{4 t^{4}}{R}$

Angular speed $ω = \frac{v}{R} = \frac{2 t^{2}}{R}$

$\tan θ = \frac{a_{t}}{a_{c}} = \frac{4 t R}{4 t^{4}} = \frac{R}{t^{3}}$

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