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1)

A particle performs linear SHM at a particular instant, velocity of the particle is 'u' and acceleration is 'α' while at another instant velocity is 'v' and acceleration is 'β  ( 0 <α < β ). The distance between the two positions is 


A) u2v2α+β

B) u2+v2α+β

C) u2v2αβ

D) u2+v2αβ

Answer:

Option A

Explanation:

Let  the distance be p when velocity is u and acceleration α.

 Let the distance  q when velocity is v and acceleration β.

 If ω  is the angular frequency  , then 

α=ω2p   ans β=ω2q

       α+β= ω2(p+q)      ........(i)

 Also,    u2=ω2A2ω2p2

and    v2=ω2A2ω2q2

    v2u2=ω2(p2q2)

 v2u2=ω2(pq)(p+q)    .........(ii)

 by Eqs .(i) and (ii), we get

v2u2=(pq)(α+β)

    pq=v2u2α+β  or   qp=u2v2α+β