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Question

The distance of a particle moving on a circular path of radius 12 m measured from a fixed point on the circle and measured along the circle is given by S=2t3 (in metres). The ratio of its tangential to centripetal acceleration at t=2 s is

A
1:1
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B
1:2
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C
2:1
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D
3:1
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Solution

The correct option is B 1:2
Tangential acceleration is given by,

at=dvdt=ddt(dsdt)

S=2 t3

at=ddt(6t2)

or at=12t ....(i)

The centripetal acceleration is given by,

ac=v2R

or ac=(dsdt)2R=(6t2)2R

ac=36t412

or ac=3 t4 ......(ii)

The ratio of at to centripetal acceleration (ac) will be,

atac=12 t3 t4

atac=4t3

Putting t=2 s we get,

atac=48

atac=12
Why this Question?
Caution: Beware!!! In problems involving variable quantities do not take ratio by substituting the values in function.
Rather simplify down the ratio to last stage then substitute the value of parameter like time.

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