Exams › NEET › Physics

The position vector of a particle R̅ as a function of time is given by: R̅ = 4sin(2πt)î + 4cos(2πt)ĵ Where R is in meter, t in seconds and î and ĵ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

1. Magnitude of acceleration vector is v²/R, where v is the velocity of particle
2. Magnitude of the velocity of particle is 8 meter/second
3. Path of the particle is a circle of radius 4 meter
4. Acceleration vector is along R̅

Correct answer: Magnitude of the velocity of particle is 8 meter/second

Solution

The magnitude of the velocity is given by |v̅| = √(vx² + vy²), where vx = d(4sin(2πt))/dt and vy = d(4cos(2πt))/dt. Calculating, |v̅| = 8π m/s, not 8 m/s. Hence, option B is incorrect.

Related NEET Physics questions

• A block is thrown with a velocity of \( 2 m / s \) (relative to ground) on a belt, which is moving with velocity \( 4 m / s \) in opposite direction of the initial velocity of block. If the block stops slipping on the belt after \( 4 s \) of the throwing then choose the correct statement(s) This question has multiple correct options
• Due to air a falling body faces a resistive force proportional to square of velocity \( v, \) consequently its effective downward acceleration is reduced and is given by \( a=g-k v^{2} \) where \( k= \) \( 0.002 m^{-1} . \) The terminal velocity of the falling body is \( (\operatorname{in} \mathrm{m} / \mathrm{s}) \)
• In the two dimensional motions:
• A ball is thrown from rear end of the compartment of train to the front end which is moving at a constant horizontal velocity. An observer \( \boldsymbol{A} \) sitting in compartment and another observer \( B \) standing on the ground draw the trajectory. They will have
• Two forces of 3 N and 4 N act at right angles to each other on a body, as shown in the figure. The magnitude of their resultant is:
• There are three particles shown in the figure as I, II and III. The velocity and acceleration vectors associated with the motion of three particles are shown. Which of the above could represent the velocity and acceleration vectors for a projectile following a parabolic path? I. II. III.

⚔️ Practice NEET Physics free + battle 1v1 →