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from objective 2 que no.10 The accelerations of a particle as seen from two frames S 1 and S 2 have equal magnitude 4m/s 2 . (a)The frames must be at rest with respect to each other. (b)The frames may be moving with respect to each other but neither should be accelerated with respect to each other. (c)The acceleration of S 2 with respect to S 1 may either be zero or 8m/s 2 . (d)The acceleration of S 2 with respect S 1 may be anything b/w zero and 8m/s 2 . ans-d i need explanation

from objective 2 que no.10


The accelerations of a particle as seen from two frames S1 and S2 have equal magnitude 4m/s2.


(a)The frames must be at rest with respect to each other.


(b)The frames may be moving with respect to each other but neither should be accelerated with respect to each other.


(c)The acceleration of S2 with respect to S1 may either be zero or 8m/s2.


(d)The acceleration of S2 with respect S1 may be anything b/w zero and 8m/s2.


ans-d


i need explanation

Grade:12th Pass

2 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Suchita,

 

As acn of particle (say p) wrt frames S1 and S2 has mag of 4m/s^2.

We write Ap/s1 = 4*[x1(i) + y1(j)]. Where x1(i)+y1(j) is a unit vector.

And similarly Ap/s2 = 4*[x2(i) + y2(j)]. Where x2(i) + y2(j) is another unit vector.

 

So now As2/s1 = Ap/s1 - Ap/s2 ----------- [this is because acn Ap/s1 = Ap - As1, in the vector notation]

so ie = 4[unit vec 1 - unit vec 2] = 4[a-b] {where unit vectors are denoted by a and b}.

So the mag of acn is |As2/s1| = 4|a-b| ----------(Note that |a|

Consider |a-b|2 = (a-b)dot(a-b) = |a|2+|b|2-2(|a|*|b|*cosx) = 2-2cosx = 2(1-cosx) = 2*2*sin2x/2 = 4sin2x/2

So |a-b| = |2sinx/2|.

And hence |As2/s1| = 8|sin(x/2)|

And clearly |sinx/2| lies between 0 to 1. And hence answer (D).

 

Also note, the above method is a general approach. For special cases of S1, and S2, and the particle moving along the same straight line, angle between a and b could be 0 or 180. And hence x/2 can be 0 or 90. (In this case the answer would be (C)).

 

Hope that helps.

 

All the best.

Regards,

Ashwin (IIT Madras).

Aditya Raj
14 Points
9 years ago

consider a stationary particle.

s1 is moving with yhat particle with a=4ms-2

s2 is moving with a=4ms-2

both frames r moving with an angleΦ now Φ can lie btween 0 to 180 so they can move wrt each other with minimum 0 relative acc.maximum or 8ms-2 .

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