Distance of a particle moving on a circle of radius 12 ,m measured from a fixed point on circle and

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3-2.Motion in Plane

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The distance of a particle moving on a circle of radius $12 \,m$ measured from a fixed point on the circle and measured along the circle is given by $s=2 t^3$ (in meters). The ratio of its tangential to centripetal acceleration at $t=2 \,s$ is .........

A

$1: 1$

B

$1: 2$

C

$2: 1$

D

$3: 1$

Solution

(b)

$S =2 t ^3$ given

$\frac{d s}{d t}=6 t^2 \Rightarrow v=6 t^2$

At $t =2 s \quad v =24 m / s$

Centripetal acc. $=\frac{ v ^2}{ R }=\frac{24 \times 24}{12}=48$

$\frac{ d ^2 s }{ dt ^2}= a _{ t }=$ Tangential acc. $=12 t$

$\operatorname{At} t=2 \sec \quad a_t=24$

$\therefore \frac{a_t}{a_c}=\frac{24}{48}=1: 2$

Standard 11

Physics

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