(a) A particle P moves along the eurve with polar oquation re a, 02- where a is a positive constant, in such a way that the tranyverse component of the accelerat. always eu, Slaw that de -k k where k is a constant. (i) di dr is constant. de (ii) Hence, show that the radial component of the acceleration is inverscly proportional to

Elements Of Electromagnetics
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Answer Q5a

5.
(a)
A particle P moves along the curve with polar equation re - a, A2.
where a is a positive constant, in such a way that the transverse component of the acceleration is
atways zau. Slnow ilsat
de
= k where k is a constant
dr
(i)
dr
is constant.
di
(ii)
Hence, show that the radial component of the acceleration is inverscly proportional to
The acceleration of a particle Q moving in the plane of the coordinale axes OX, OY is-(xi + yi)
where o is a positive constant and i and j are unit vcclurs along OX and OY respectively.
At time t-0, Q passes through the point A with position vector 5Ai while moving with velocity
3aaj ms".
(b)
(i)
Show that the position vector of Q at time t is (SAeos t)i + (3Asin wt)j.
(i)
Find the Cartesian equation of the path of Q.
(iii)
Find the time taken for Q to retum to A.
Transcribed Image Text:5. (a) A particle P moves along the curve with polar equation re - a, A2. where a is a positive constant, in such a way that the transverse component of the acceleration is atways zau. Slnow ilsat de = k where k is a constant dr (i) dr is constant. di (ii) Hence, show that the radial component of the acceleration is inverscly proportional to The acceleration of a particle Q moving in the plane of the coordinale axes OX, OY is-(xi + yi) where o is a positive constant and i and j are unit vcclurs along OX and OY respectively. At time t-0, Q passes through the point A with position vector 5Ai while moving with velocity 3aaj ms". (b) (i) Show that the position vector of Q at time t is (SAeos t)i + (3Asin wt)j. (i) Find the Cartesian equation of the path of Q. (iii) Find the time taken for Q to retum to A.
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