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Asked by Dnyanutheurkar | 12 Sep, 2021, 14:59: PM

Expert Answer

Radius vector

begin mathsize 14px style r with rightwards arrow on top space equals space left parenthesis space 10 space cos omega t space i with hat on top space minus space 10 space sin omega t space j with hat on top space right parenthesis space m end style

............................ (1)

Magnitude of radius vector

begin mathsize 14px style open vertical bar r with rightwards arrow on top close vertical bar space equals space square root of 100 left parenthesis cos squared omega t space plus space sin squared omega t right parenthesis end root space equals space 10 space m end style

......................(2)

velocity

begin mathsize 14px style v with rightwards arrow on top space equals space fraction numerator d r with rightwards arrow on top over denominator d t end fraction equals omega left parenthesis space minus 10 space sin omega t space i with hat on top space space minus space 10 space cos omega t space j with hat on top space right parenthesis space m divided by s end style

.......................(3)

magnitude of velocity

begin mathsize 14px style open vertical bar v close vertical bar space equals space omega square root of 100 left parenthesis sin squared omega t space plus space cos squared omega t space right parenthesis end root space equals space 10 space omega space m divided by s end style

.........................(4)

Acceleration

begin mathsize 14px style a with rightwards arrow on top space equals space fraction numerator d space v with rightwards arrow on top over denominator d space t end fraction space equals space omega squared space left parenthesis negative 10 space cos omega t space i with hat on top space plus space 10 space sin omega t space j with hat on top space right parenthesis space equals space minus omega squared space r with rightwards arrow on top space m divided by s squared end style

........................(5)

Magnitude of acceleration

begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar space equals space omega squared open vertical bar r with rightwards arrow on top close vertical bar space equals space 10 omega squared space m divided by s squared end style

....................... (6)

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Statement-1 :- Centripetal acceleration at t = 1 s is 10ω²

Above statement is true as per eqn.(5) and (6) .

Acceleration is directed in direction of radius vector and its magnitude is 10ω² i.e. independent of time

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Statement-2 :- Centripetal acceleration at t = 2 s is 40ω²

Above statement is false because magnitude of acceleration is always 10ω² and is independent of time.

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Statement-3 :- Speed of particle is constant

Above statement is true because speed is magnitude of velocity that is constant 10ω as per eqn.(4)

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Statement-4 :- Acceleration is directed towards origin

Above statement is true. we determined acceleration in eqn.(5) .

we see that direction of acceleration is in the direction of radius vector.

Negative sign shows acceleration is directed towards origin.

Answered by Thiyagarajan K | 12 Sep, 2021, 16:14: PM

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