Motion in a Plane - Result Question 43

46. The position vector of a particle R as a function of time is given by:

R=4sin(2πt)i^+4cos(2πt)j^

Where R is in meter, t in seconds and i^ and j^ denote unit vectors along x-and y-directions, respectively.

Which one of the following statements is wrong for the motion of particle?

[2015 RS]

(a) Magnitude of acceleration vector is v2R, where v is the velocity of particle

(b) Magnitude of the velocity of particle is 8 meter/second

(c) path of the particle is a circle of radius 4 meter.

(d) Acceleration vector is along R

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Answer:

Correct Answer: 46. (b)

Solution:

  1. (b) Here, x=4sin(2πt)

(i)y=4cos(2πt)

Squaring and adding equation (i) and (ii) x2+y2=42R=4

Motion of the particle is circular motion, acceleration vector is along R and its magnitude =V2R

Velocity of particle, V=ωR=(2π)(4)=8π



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