Verified Solution • 2025–26 Session moderate

QNEET-2016-Ph-1076: NEET 2016 Physics - Class 11 NEET-2016-Ph-1076 Solution: A particle moves so that its position vector is given by \( {r} …

A particle moves so that its position vector is given by r⃗=cos⁡ωtx^+sin⁡ωty^\vec{r} = \cos\omega t\hat{x} + \sin\omega t\hat{y} where ω\omega is a constant. Which of the following is true? Velocity is perpendicular to r and acceleration is directed towards the origin. Velocity is perpendicular to r and acceleration is directed away from the origin. Velocity and acceleration both are perpendicular to r Velocity and acceleration both are parallel to r

Multiple Choice Options

  • A Velocity is perpendicular to r→\overrightarrow r r and acceleration is directed towards the origin.
  • B Velocity is perpendicular to r→\overrightarrow r r and acceleration is directed away from the origin.
  • C Velocity and acceleration both are perpendicular to r→\overrightarrow r r
  • D Velocity and acceleration both are parallel to r→\overrightarrow r r

Step-by-Step Verified Solution

r _ = cos _ _ t x ^ + sin _ t y ^ , _ v _ = _ _ sin _ _ t x ^ + _ cos _ _ t y ^ and a _ = _ _ 2 cos _ _ t x ^ _ _ 2 sin _ _ t y ^ = _ _ 2 r _ r _ . v _ = 0 _ r _ _ v _ As position vector ( r _ ) is directly away from the origin, so, acceleration ( _ _ 2 r _ ) is directed towards the origin.

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