The position vector r of a particle is given by r = ( 3 cos 4 t ) i ^ + ( 3 sin 4 t ) j ^ . Which of the following statement(s) is/are correct ?

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Physics - Circular Motion Question with Solution | TestHub

PhysicsCircular MotionKinematicsMedium2 minQB

PhysicsMediummultiple choice

The position vector $r$ of a particle is given by $r = (3 cos 4 t) \hat{i} + (3 sin 4 t) \hat{j}$ . Which of the following statement(s) is/are correct ?

Options:(select one or more)

Answer:

B, C

Solution:

$r = 3 cos (4 t) \hat{i} + 3 sin (4 t) \hat{j}$ describes circular motion of radius 3.

$v = \frac{d r}{d t} = - 12 sin (4 t) \hat{i} + 12 cos (4 t) \hat{j}$

$r \cdot v = 0$ . Velocity is perpendicular to position: B true; A false.

$a = \frac{d v}{d t} = - 48 cos (4 t) \hat{i} - 48 sin (4 t) \hat{j} = - 16 r$

Acceleration points to the origin: C true; D false.

Subject:PhysicsTopic:Circular MotionSubtopic:Kinematics

⏱ 2mℹ️ Source: QB

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